Solve the following problem. A 20-foot flag pole casts an 8-foot shadow. What is the shadow length of a 30 foot flagpole at the same time?

Show your complete solutions by creating a diagram that represents the situation and coming up with a solution for each. 1. To measure the height of the cloud cover at an airport, a worker shines a spotlight upward at an angle 75° from the horizontal. An observer 600 m away measures the angle of elevation to the spot of light to be 45°. Find the height h of the cloud cover.   2. A 600-ft guy wire is attached to the top of a communications tower. If the wire makes an angle of 65° with theground, how tall is the communications tower?   3. To measure the height of an inaccessible cliff on the opposite side of a river, a surveyor makes the measurements shown in the figure at the right. Find the height of the cliff.

James is trying to determine the height of a building, so he uses a street sign as a reference. The street sign is 6 feet tall and casts a shadow of 5 feet. The two triangles formed in the picture above are similar. If the building casts a shadow of 35 feet, what is the height of the building? O A. 41 feet В. 175 feet Oc. 47 feet D. 42 feet

The second hand on a clock completes one full revolution per minute. If that second hand has length 15 cm, then what it is linear speed? 15 cm per minute 15T cm per minute O 30 cm per minute 30T cm per minute

22. Physical Therapy. To rehabilitate her knee, an athlete does leg extensions. Her goal is to regain a full 90° range of motion in this exercise. Use the information in the illustration to determine her current range of motion in degrees and the number of degrees of improvement she still needs to make. She needs to extend this much more. Current range of motion. This angle is four times larger than the other.

Two ships left Port Hope on Lake Ontario at the same time. One travelled at 12 km/h on a course of 235 degrees. The other travelled at 15 km/h on a course of 105 degrees. How far apart were the ships after four hours to the nearest kilometre?

Show your complete solution.

This diagram shows 2 flag poles that are 5 m tall. The distance from the top of the left pole to the base of the right pole is 14 m. What is the distance between the 2 flag poles? Answer to the nearest metre. 14m 5m Select one: a. 12m b. 13m с. 10m d. 15m

Kolby needs to fix a leaky roof on his mom's house but doesn't own a ladder. He thinks that a 25-foot ladder will be long enough to reach the roof, but he needs to be sure before he spends the money to buy one. He chooses a point P on the ground where he can visually align the roof of his 4.25 ft tall car with the edge of the roof of the house. If point P is 8.5 ft from the car and the car is 23 ft from the house, will the 25-foot ladder be tall enough?

I can make the drawing, but I'm not sure if I'm doing it right. I think I can make A = 30 degrees for the segment that is twice as long, but I'm not sure if that's right.