Answered: Refer to right triangle ABC in which C…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Additional Topics In Trigonometry

Section3.2: Law Of Cosines

Problem 2ECP: Given A=80,b=16 meters, and c=12 meters, find the remaining angles and side of the triangle.

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Refer to right triangle ABC in which C = 90°. Solve each triangle.

B=22 ⁰, b = 320

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Expert Solution

Given,

$B = 22 °, C = 90 ° & b = 320$

The triangle is,

Now since the sum of all the angles of triangle is $180 °$ , therefore

$∠ A + ∠ B + ∠ C = 180 ° \Rightarrow ∠ A + 22 ° + 90 ° = 180 ° \Rightarrow ∠ A = 68 °$

Now,

$\sin 22 ° = \frac{320}{A B} \Rightarrow A B = \frac{320}{\sin 22 °} \Rightarrow A B = 854.229492$

$\tan 22 ° = \frac{320}{B C} \Rightarrow B C = \frac{320}{\tan 22 °} \Rightarrow B C = 792.027793$

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