Question

Solve the right triangle, ΔABC, for the missing side and angles to the nearest tenth given sides a = 14.9 and b = 17.5.

A. A = 31.6 , B = 58.4 , c = 9.2
B. A = 49.6 , B = 40.4 , c = 23
C. A = 40.4 , B = 49.6 , c = 23
D. A = 40.4 , B = 49.6 , c = 9.2

Answer 1

C. A = 40.4 , B = 49.6 , c = 23

Explanation:

First, we need to get the c using the pythagoras theorem;

c² = a²+b²

c² = 14.9²+17.5²

c² = 222.01 + 306.25

c² = 528.26

c = 22.98

c ≈ 23

Using the sin rule;

a/Sin<A = c/sin<C

14.9/sin<A = 23/sin90

14.9/sin<A = 23

sin<A = 14.9/23

sin <A = 0.6478

<A = arcsin(0.6478)

<A = 40.4degrees

Also, <A + <B + <C = 180

40.4 + <B + 90 = 180

<B = 180 - 130.4

<B = 49.6degrees