Question

use the given measurements to solve each triangle. round to the nearest tenth please help me r=11.6

Answer 1

EXPLANATION

Given the triangle, we can calculate the value of the other angles by applying the Law of Sines as we already know,

$\frac{\sin 89}{11.5}=\frac{\sin Q}{9}$

Multiplying both sides by 9:

$9\cdot\frac{\sin89}{11.5}=\sin Q$

Switching sides:

$\sin Q=9\cdot\frac{\sin 89}{11.5}$

Simplifying:

$\sin Q=9\cdot0.0869=0.78$

Applying sin-1 to both sides:

$Q=\sin ^{-1}(0.78)$

Computing the argument:

$Q=51.48^o$

Applying the Triangles Sum of Interior Angles Theorem give us the following relationship:

89 + 51.48 + P = 180

Adding like terms:

140.48 + P = 180

Subtracting 140.48 to both sides:

P = 180 - 140.48 = 39.52 degrees

The answers are:

Q=51.5°

P = 39.5° ---> Rounding to the nearest tenth