Question

Laws of Sines with find the angle.

Find each measurement indicated. Round your answers to the nearest tenth. Part 1
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Answer 1

1. H ≈ 49.1°

2. F ≈ 38.0°

3. R ≈ 17.0°

Explanation:

1.

We need to find angle H, which is the third angle. We are given two sides and an angle, so we can use the Law of Sines to solve.

The Law of Sines states that for a triangle with side lengths a, b, and c and angles A, B, and C:

`(a)/(sinA) =(b)/(sinB) =(c)/(sinC)`

Here, we can say that a = 22, b = 27, and B = 68. We want to find "A", which is the same angle as H:

`(a)/(sinA) =(b)/(sinB)`

`(22)/(sinH) =(27)/(sin(68))`

Solve for H:

H ≈ 49.1°

2.

Use the Law of Sines again (use the same method as above):

`(17)/(sin(108)) =(11)/(sin(F))`

Solve for F:

F ≈ 38.0°

3.

Use the Law of Sines again (use the same method as before):

`(9)/(sin(26)) =(6)/(sin(R))`

Solve for R:

R ≈ 17.0°

Answer 2

A divide by sin A = b divide by sin B
1. 27 divide by sin 68=22 divide by sin x
Sin x=sin 68 times 22 divide by 27
Sinx=0.65696
X=71.7 degrees