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,

`(\sin 89)/(11.5)=(\sin Q)/(9)`

Multiplying both sides by 9:

`9\cdot(\sin89)/(11.5)=\sin Q`

Switching sides:

`\sin Q=9\cdot(\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