Precalculus
Precalculus
9th Edition
ISBN: 9780321716835
Author: Michael Sullivan
Publisher: Addison Wesley
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Chapter 8.2, Problem 40AYU

Finding the Height of a Mountain Use the illustration in Problem 37 to find the height QD of the mountain.

Expert Solution
Check Mark
To determine

To find: The height of the mountain.

Answer to Problem 40AYU

Solution:

620.9 feet

Explanation of Solution

Given:

Height of the mountain

To find the length of the span of a proposed ski lift from P to Q, a surveyor measures DPQ to be 25 and then walks back a distance of 1000 feet to R and measures PRQ to be 15

Precalculus, Chapter 8.2, Problem 40AYU

Formula used:

sinAa = sinBb = sinCc

A + B + C = 180

Calculation:

In the above figure angle QPD = 25 and the angle eat D is 900 so the angle at Q will be 650 in the triangle QPD

And from the above solution we know that QP value

So QP = 1490.48 feet

From the figure we clearly known that QP is hypotenuse and QD is opposite side so we can use sin angle to find the value of opposite side

So sin25 = QDQP = QD1490.48

Sin25  0.42

So QD = sin25° × 1490.48  629.90feet

So the height of the mountain is 629.90feet

Chapter 8 Solutions

Precalculus

Ch. 8.1 - In Problems 9-18, find the exact value of the six...Ch. 8.1 - In Problems 9-18, find the exact value of the six...Ch. 8.1 - In Problems 9-18, find the exact value of the six...Ch. 8.1 - In Problems 9-18, find the exact value of the six...Ch. 8.1 - In Problems 9-18, find the exact value of the six...Ch. 8.1 - Prob. 16AYUCh. 8.1 - In Problems 9-18, find the exact value of the six...Ch. 8.1 - Prob. 18AYUCh. 8.1 - In Problems 19-28, find the exact value of each...Ch. 8.1 - In Problems 19-28, find the exact value of each...Ch. 8.1 - In Problems 19-28, find the exact value of each...Ch. 8.1 - Prob. 22AYUCh. 8.1 - In Problems 19-28, find the exact value of each...Ch. 8.1 - In Problems 19-28, find the exact value of each...Ch. 8.1 - In Problems 19-28, find the exact value of each...Ch. 8.1 - In Problems 19-28, find the exact value of each...Ch. 8.1 - In Problems 19-28, find the exact value of each...Ch. 8.1 - In Problems 19-28, find the exact value of each...Ch. 8.1 - In Problems 29-42, use the right triangle shown...Ch. 8.1 - In Problems 29-42, use the right triangle shown...Ch. 8.1 - In Problems 29-42, use the right triangle shown...Ch. 8.1 - Prob. 32AYUCh. 8.1 - In Problems 29-42, use the right triangle shown...Ch. 8.1 - Prob. 34AYUCh. 8.1 - Prob. 35AYUCh. 8.1 - In Problems 29-42, use the right triangle shown...Ch. 8.1 - In Problems 29-42, use the right triangle shown...Ch. 8.1 - Prob. 38AYUCh. 8.1 - In Problems 29-42, use the right triangle shown...Ch. 8.1 - In Problems 29-42, use the right triangle shown...Ch. 8.1 - Prob. 41AYUCh. 8.1 - Prob. 42AYUCh. 8.1 - Geometry The hypotenuse of a right triangle is 5...Ch. 8.1 - Geometry The hypotenuse of a right triangle is 3...Ch. 8.1 - Geometry A right triangle has a hypotenuse of...Ch. 8.1 - Geometry A right triangle has a hypotenuse of...Ch. 8.1 - Geometry A right triangle contains a 25 angle. (a)...Ch. 8.1 - Geometry A right triangle contains an angle of 8...Ch. 8.1 - Finding the Width of a Gorge Find the distance...Ch. 8.1 - Finding the Distance across a Pond Find the...Ch. 8.1 - The Eiffel Tower The tallest tower built before...Ch. 8.1 - Finding the Distance of a Ship from Shore A person...Ch. 8.1 - Finding the Distance to a Plateau Suppose that you...Ch. 8.1 - Finding the Reach of a Ladder A 22-foot extension...Ch. 8.1 - Finding the Angle of Elevation of the Sun At 10 AM...Ch. 8.1 - Directing a Laser Beam A laser beam is to be...Ch. 8.1 - Finding the Speed of a Truck A state trooper is...Ch. 8.1 - Security A security camera in a neighborhood bank...Ch. 8.1 - Parallax One method of measuring the distance from...Ch. 8.1 - Parallax See Problem 59. 61 Cygni, sometimes...Ch. 8.1 - Washington Monument The angle of elevation of the...Ch. 8.1 - Finding the Length of a Mountain Trail A straight...Ch. 8.1 - Finding the Bearing of an Aircraft A DC-9 aircraft...Ch. 8.1 - Prob. 64AYUCh. 8.1 - Niagara Falls Incline Railway Situated between...Ch. 8.1 - Willis Tower Willis Tower in Chicago is the second...Ch. 8.1 - Constructing a Highway A highway whose primary...Ch. 8.1 - Photography A camera is mounted on a tripod 4 feet...Ch. 8.1 - Finding the Distance between Two Objects A blimp,...Ch. 8.1 - Hot-Air Balloon While taking a ride in a hot-air...Ch. 8.1 - Mt. Rushmore To measure the height of Lincoln’s...Ch. 8.1 - The CN Tower The CN Tower, located in Toronto,...Ch. 8.1 - Chicago Skyscrapers The angle of inclination from...Ch. 8.1 - Estimating the Width of the Mississippi River A...Ch. 8.1 - Finding the Pitch of a Roof A carpenter is...Ch. 8.1 - Shooting Free Throws in Basketball The eyes of a...Ch. 8.1 - Geometry Find the value of the angle in degrees...Ch. 8.1 - Surveillance Satellites A surveillance satellite...Ch. 8.1 - Calculating Pool Shots A pool player located at X...Ch. 8.1 - Prob. 80AYUCh. 8.1 - Prob. 81AYUCh. 8.1 - Prob. 82AYUCh. 8.1 - Prob. 83AYUCh. 8.2 - The difference formula for the sine function is...Ch. 8.2 - Prob. 2AYUCh. 8.2 - Prob. 3AYUCh. 8.2 - Prob. 4AYUCh. 8.2 - Prob. 5AYUCh. 8.2 - Prob. 6AYUCh. 8.2 - Prob. 7AYUCh. 8.2 - Prob. 8AYUCh. 8.2 - In Problems 9-16, solve each triangle.Ch. 8.2 - In Problems 9-16, solve each triangle.Ch. 8.2 - In Problems 9-16, solve each triangle.Ch. 8.2 - In Problems 9-16, solve each triangle.Ch. 8.2 - In Problems 9-16, solve each triangle.Ch. 8.2 - In Problems 9-16, solve each triangle.Ch. 8.2 - In Problems 9-16, solve each triangle.Ch. 8.2 - In Problems 9-16, solve each triangle.Ch. 8.2 - In Problems , solve each triangle. Ch. 8.2 - In Problems 17-24, solve each triangle. A= 50 ,...Ch. 8.2 - In Problems 1926, solve each triangle....Ch. 8.2 - In Problems 17-24, solve each triangle. A= 70 ,...Ch. 8.2 - In Problems 17-24, solve each triangle. A= 110 ,...Ch. 8.2 - In Problems 17-24, solve each triangle. B= 10 ,...Ch. 8.2 - In Problems 17-24, solve each triangle. A= 40 ,...Ch. 8.2 - In Problems 17-24, solve each triangle. B= 20 ,...Ch. 8.2 - In Problems 25-36, two sides and an angle are...Ch. 8.2 - In Problems 25-36, two sides and an angle are...Ch. 8.2 - In Problems 2738, two sides and an angle are...Ch. 8.2 - In Problems 25-36, two sides and an angle are...Ch. 8.2 - In Problems , two sides and an angle are given....Ch. 8.2 - In Problems 25-36, two sides and an angle are...Ch. 8.2 - In Problems 25-36, two sides and an angle are...Ch. 8.2 - In Problems 25-36, two sides and an angle are...Ch. 8.2 - In Problems , two sides and an angle are given....Ch. 8.2 - In Problems 25-36, two sides and an angle are...Ch. 8.2 - In Problems 2738, two sides and an angle are...Ch. 8.2 - In Problems 25-36, two sides and an angle are...Ch. 8.2 - Prob. 37AYUCh. 8.2 - Prob. 38AYUCh. 8.2 - Finding the Length of a Ski Lift Consult the...Ch. 8.2 - Finding the Height of a Mountain Use the...Ch. 8.2 - Finding the Height of an Airplane An aircraft is...Ch. 8.2 - Finding the Height of the Bridge over the Royal...Ch. 8.2 - Prob. 43AYUCh. 8.2 - Prob. 44AYUCh. 8.2 - Prob. 45AYUCh. 8.2 - Prob. 46AYUCh. 8.2 - Prob. 47AYUCh. 8.2 - Prob. 48AYUCh. 8.2 - Prob. 49AYUCh. 8.2 - Prob. 50AYUCh. 8.2 - Prob. 51AYUCh. 8.2 - Prob. 52AYUCh. 8.2 - Prob. 53AYUCh. 8.2 - Prob. 54AYUCh. 8.2 - Prob. 55AYUCh. 8.2 - Prob. 56AYUCh. 8.2 - Prob. 57AYUCh. 8.2 - Prob. 58AYUCh. 8.2 - Prob. 59AYUCh. 8.2 - Prob. 60AYUCh. 8.2 - Prob. 61AYUCh. 8.2 - Prob. 62AYUCh. 8.2 - Make up three problems involving oblique...Ch. 8.2 - Prob. 64AYUCh. 8.2 - What do you do first if you are asked to solve a...Ch. 8.3 - Write the formula for the distance d from P 1 =( x...Ch. 8.3 - If is an acute angle, solve the equation cos= 2 2...Ch. 8.3 - If three sides of a triangle are given, the Law of...Ch. 8.3 - Prob. 4AYUCh. 8.3 - Prob. 5AYUCh. 8.3 - True or False Given only the three sides of a...Ch. 8.3 - True or False The Law of Cosines states that the...Ch. 8.3 - True or False A special case of the Law of Cosines...Ch. 8.3 - In Problems 9-16, solve each triangle.Ch. 8.3 - In Problems 9-16, solve each triangle.Ch. 8.3 - In Problems 9-16, solve each triangle.Ch. 8.3 - In Problems 9-16, solve each triangle.Ch. 8.3 - In Problems 9-16, solve each triangle.Ch. 8.3 - In Problems 9-16, solve each triangle.Ch. 8.3 - In Problems 9-16, solve each triangle.Ch. 8.3 - In Problems 9-16, solve each triangle.Ch. 8.3 - In Problems 17-32, solve each triangle. a=3 , b=4...Ch. 8.3 - In Problems 17-32, solve each triangle. a=2 , c=1...Ch. 8.3 - In Problems 1732, solve each triangle....Ch. 8.3 - In Problems 17-32, solve each triangle. a=6 , b=4...Ch. 8.3 - In Problems solve each triangle. Ch. 8.3 - In Problems 17-32, solve each triangle. b=4 , c=1...Ch. 8.3 - In Problems solve each triangle. Ch. 8.3 - In Problems 17-32, solve each triangle. a=3 , c=2...Ch. 8.3 - In Problems solve each triangle. Ch. 8.3 - In Problems 17-32, solve each triangle. a=4 , b=5...Ch. 8.3 - In Problems 17-32, solve each triangle. a=2 , b=2...Ch. 8.3 - In Problems 17-32, solve each triangle. a=3 , b=3...Ch. 8.3 - In Problems 1732, solve each triangle....Ch. 8.3 - In Problems 17-32, solve each triangle. a=4 , b=3...Ch. 8.3 - In Problems 17-32, solve each triangle. a=10 , b=8...Ch. 8.3 - In Problems 17-32, solve each triangle. a=9 , b=7...Ch. 8.3 - In Problems 33-42, solve each triangle using...Ch. 8.3 - In Problems 33-42, solve each triangle using...Ch. 8.3 - In Problems 33-42, solve each triangle using...Ch. 8.3 - Prob. 36AYUCh. 8.3 - Prob. 37AYUCh. 8.3 - In Problems 33-42, solve each triangle using...Ch. 8.3 - Prob. 39AYUCh. 8.3 - Prob. 40AYUCh. 8.3 - Prob. 41AYUCh. 8.3 - Prob. 42AYUCh. 8.3 - Distance to the Green A golfer hits an errant tee...Ch. 8.3 - Navigation An airplane flies due north from Ft....Ch. 8.3 - Avoiding a Tropical Storm A cruise ship maintains...Ch. 8.3 - Revising a Flight Plan In attempting to fly from...Ch. 8.3 - Major League Baseball Field A major league...Ch. 8.3 - Little League Baseball Field According to Little...Ch. 8.3 - Finding the Length of a Guy Wire The height of a...Ch. 8.3 - Finding the Length of a Guy Wire A radio tower 500...Ch. 8.3 - Prob. 51AYUCh. 8.3 - Prob. 52AYUCh. 8.3 - Prob. 53AYUCh. 8.3 - Prob. 54AYUCh. 8.3 - Prob. 55AYUCh. 8.3 - Prob. 56AYUCh. 8.3 - Prob. 57AYUCh. 8.3 - Prob. 58AYUCh. 8.3 - Prob. 59AYUCh. 8.3 - Prob. 60AYUCh. 8.3 - Prob. 61AYUCh. 8.3 - Prob. 62AYUCh. 8.3 - Prob. 63AYUCh. 8.4 - The area K of a triangle whose base is b and whose...Ch. 8.4 - If two sides a and b and the included angle C are...Ch. 8.4 - The area K of a triangle with sides a , b , and c...Ch. 8.4 - Prob. 4AYUCh. 8.4 - Prob. 5AYUCh. 8.4 - Prob. 6AYUCh. 8.4 - Prob. 7AYUCh. 8.4 - Prob. 8AYUCh. 8.4 - Prob. 9AYUCh. 8.4 - Prob. 10AYUCh. 8.4 - Prob. 11AYUCh. 8.4 - Prob. 12AYUCh. 8.4 - Prob. 13AYUCh. 8.4 - Prob. 14AYUCh. 8.4 - Prob. 15AYUCh. 8.4 - Prob. 16AYUCh. 8.4 - Prob. 17AYUCh. 8.4 - Prob. 18AYUCh. 8.4 - Prob. 19AYUCh. 8.4 - Prob. 20AYUCh. 8.4 - Prob. 21AYUCh. 8.4 - Prob. 22AYUCh. 8.4 - Prob. 23AYUCh. 8.4 - Prob. 24AYUCh. 8.4 - Prob. 25AYUCh. 8.4 - Prob. 26AYUCh. 8.4 - Prob. 27AYUCh. 8.4 - Prob. 28AYUCh. 8.4 - Prob. 29AYUCh. 8.4 - Prob. 30AYUCh. 8.4 - Prob. 31AYUCh. 8.4 - Prob. 32AYUCh. 8.4 - Prob. 33AYUCh. 8.4 - Prob. 34AYUCh. 8.4 - Cost of a Triangular Lot The dimensions of a...Ch. 8.4 - Prob. 36AYUCh. 8.4 - Prob. 37AYUCh. 8.4 - Prob. 38AYUCh. 8.4 - Prob. 39AYUCh. 8.4 - Prob. 40AYUCh. 8.4 - Prob. 41AYUCh. 8.4 - Prob. 42AYUCh. 8.4 - Prob. 43AYUCh. 8.4 - Prob. 44AYUCh. 8.4 - Prob. 45AYUCh. 8.4 - Prob. 46AYUCh. 8.4 - Prob. 47AYUCh. 8.4 - Prob. 48AYUCh. 8.4 - Prob. 49AYUCh. 8.4 - Prob. 50AYUCh. 8.4 - Prob. 51AYUCh. 8.4 - Prob. 52AYUCh. 8.4 - Prob. 53AYUCh. 8.4 - Prob. 54AYUCh. 8.4 - Prob. 55AYUCh. 8.4 - Prob. 56AYUCh. 8.5 - The amplitude A and period T of f( x )=5sin( 4x )...Ch. 8.5 - Prob. 2AYUCh. 8.5 - Prob. 3AYUCh. 8.5 - Prob. 4AYUCh. 8.5 - Prob. 5AYUCh. 8.5 - Prob. 6AYUCh. 8.5 - Prob. 7AYUCh. 8.5 - Prob. 8AYUCh. 8.5 - Rework Problem 7 under the same conditions, except...Ch. 8.5 - Prob. 10AYUCh. 8.5 - Rework Problem 9 under the same conditions, except...Ch. 8.5 - Rework Problem 10 under the same conditions,...Ch. 8.5 - Prob. 13AYUCh. 8.5 - Prob. 14AYUCh. 8.5 - Prob. 15AYUCh. 8.5 - Prob. 16AYUCh. 8.5 - In Problems 15-22, the displacement (in meters) of...Ch. 8.5 - Prob. 18AYUCh. 8.5 - Prob. 19AYUCh. 8.5 - Prob. 20AYUCh. 8.5 - Prob. 21AYUCh. 8.5 - Prob. 22AYUCh. 8.5 - Prob. 23AYUCh. 8.5 - Prob. 24AYUCh. 8.5 - Prob. 25AYUCh. 8.5 - Prob. 26AYUCh. 8.5 - Prob. 27AYUCh. 8.5 - Prob. 28AYUCh. 8.5 - Prob. 29AYUCh. 8.5 - Prob. 30AYUCh. 8.5 - Prob. 31AYUCh. 8.5 - Prob. 32AYUCh. 8.5 - Prob. 33AYUCh. 8.5 - Prob. 34AYUCh. 8.5 - Prob. 35AYUCh. 8.5 - Prob. 36AYUCh. 8.5 - Prob. 37AYUCh. 8.5 - Prob. 38AYUCh. 8.5 - Prob. 39AYUCh. 8.5 - Prob. 40AYUCh. 8.5 - Prob. 41AYUCh. 8.5 - Prob. 42AYUCh. 8.5 - Prob. 43AYUCh. 8.5 - Prob. 44AYUCh. 8.5 - Prob. 45AYUCh. 8.5 - Prob. 46AYUCh. 8.5 - Prob. 47AYUCh. 8.5 - In Problems 45-50. the distance d (in meters) of...Ch. 8.5 - Prob. 49AYUCh. 8.5 - Prob. 50AYUCh. 8.5 - Loudspeaker A loudspeaker diaphragm is oscillating...Ch. 8.5 - Colossus Added to Six Flags St. Louis in 1986, the...Ch. 8.5 - Tuning Fork The end of a tuning fork moves in...Ch. 8.5 - Tuning Fork The end of a tuning fork moves in...Ch. 8.5 - Charging a Capacitor See the illustration. If a...Ch. 8.5 - The Sawtooth Curve An oscilloscope often displays...Ch. 8.5 - Prob. 57AYUCh. 8.5 - Prob. 58AYUCh. 8.5 - Prob. 59AYUCh. 8.5 - Prob. 60AYUCh. 8.5 - Prob. 61AYUCh. 8.5 - Prob. 62AYUCh. 8.5 - Prob. 63AYUCh. 8.5 - Prob. 64AYUCh. 8 - Prob. 1RECh. 8 - Prob. 2RECh. 8 - Prob. 3RECh. 8 - Prob. 4RECh. 8 - Prob. 5RECh. 8 - Prob. 6RECh. 8 - Prob. 7RECh. 8 - Prob. 8RECh. 8 - Prob. 9RECh. 8 - Prob. 10RECh. 8 - Prob. 11RECh. 8 - Prob. 12RECh. 8 - Prob. 13RECh. 8 - Prob. 14RECh. 8 - Prob. 15RECh. 8 - Prob. 16RECh. 8 - Prob. 17RECh. 8 - Prob. 18RECh. 8 - Prob. 19RECh. 8 - Prob. 20RECh. 8 - Prob. 21RECh. 8 - Prob. 22RECh. 8 - Prob. 23RECh. 8 - Prob. 24RECh. 8 - Prob. 25RECh. 8 - Prob. 26RECh. 8 - Prob. 27RECh. 8 - Prob. 28RECh. 8 - Prob. 29RECh. 8 - Prob. 30RECh. 8 - Prob. 31RECh. 8 - Prob. 32RECh. 8 - Prob. 33RECh. 8 - Prob. 34RECh. 8 - Prob. 35RECh. 8 - Prob. 36RECh. 8 - Prob. 37RECh. 8 - Prob. 38RECh. 8 - Prob. 39RECh. 8 - Prob. 40RECh. 8 - Prob. 41RECh. 8 - Prob. 42RECh. 8 - Prob. 43RECh. 8 - Prob. 44RECh. 8 - Prob. 45RECh. 8 - Prob. 46RECh. 8 - Prob. 47RECh. 8 - Prob. 48RECh. 8 - Prob. 49RECh. 8 - Prob. 50RECh. 8 - Prob. 51RECh. 8 - Prob. 52RECh. 8 - Prob. 53RECh. 8 - Prob. 54RECh. 8 - Prob. 55RECh. 8 - Prob. 56RECh. 8 - Prob. 57RECh. 8 - Prob. 58RECh. 8 - Prob. 59RECh. 8 - Prob. 60RECh. 8 - Prob. 61RECh. 8 - Prob. 62RECh. 8 - Prob. 63RECh. 8 - Prob. 64RECh. 8 - Prob. 65RECh. 8 - Prob. 66RECh. 8 - Prob. 67RECh. 8 - Prob. 68RECh. 8 - Prob. 69RECh. 8 - Prob. 70RECh. 8 - Prob. 71RECh. 8 - Prob. 72RECh. 8 - Prob. 73RECh. 8 - Prob. 74RECh. 8 - Prob. 1CTCh. 8 - Prob. 2CTCh. 8 - In Problem, use the given information to determine...Ch. 8 - Prob. 4CTCh. 8 - In Problem 35, use the given information to...Ch. 8 - Prob. 6CTCh. 8 - Prob. 7CTCh. 8 - Prob. 8CTCh. 8 - Prob. 9CTCh. 8 - 10. Find the area of the triangle described in...Ch. 8 - Prob. 11CTCh. 8 - A hot- air balloon is flying at a height of 600...Ch. 8 - Find the area of the shaded region enclosed in a...Ch. 8 - 14. Find the area of the quadrilateral shown. Ch. 8 - Prob. 15CTCh. 8 - Prob. 16CTCh. 8 - Prob. 17CTCh. 8 - Prob. 18CTCh. 8 - Prob. 1CRCh. 8 - Prob. 2CRCh. 8 - Prob. 3CRCh. 8 - Prob. 4CRCh. 8 - Prob. 5CRCh. 8 - Prob. 6CRCh. 8 - Prob. 7CRCh. 8 - Graph each of the following functions...Ch. 8 - Solve the triangle for which side a is 20, side c...Ch. 8 - Prob. 10CRCh. 8 - Prob. 11CRCh. 8 - Prob. 12CRCh. 8 - Prob. 13CRCh. 8 - Suppose that f(x)=4x+5 and g(x)=x2+5x24. Solve...
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