Question

Laws of Sines with find the angle. Find the measurement indicated. Round your answers to the nearest tenth. Part 3​

Answer 1

7. 60.1°

8. 34.0°

9. 33.1°

Explanation:

7. 7/sinA = 8/sin82

sinA = 7 × sin82/8

sinA = 0.8664845601

A = 60.05265736

8. 14/sin37 = 13/sinB

sinB = 0.5588282358

B = 33.97480112

9. 10/sinC = 17/sin68

sinC = 10 × sin68/17

sinC = 0.5454022674

C = 33.05215746

Answer 2

7. A ≈ 60.1°

8. B ≈ 34.0°

9. C ≈ 33.1°

Explanation:

7.

The Law of Sines states that for a triangle with lengths a, b, and c and angles A, B, and C:
`(a)/(sinA)= (b)/(sinB) =(c)/(sinC)`.

Here, we can say that a = 7, b = 8, and B = 82, and we want to find A. Plug these values in:

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

`(7)/(sinA) =(8)/(sin(82))`

Solve for A:

A ≈ 60.1°

8.

Again, use the Law of Sines as above:

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

`(14)/(sin(37)) =(13)/(sinB)`

Solve for B:

B ≈ 34.0°

9.

Use the Law of Sines as above:

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

`(17)/(sin(68)) =(10)/(sinC)`

Solve for C:

C ≈ 33.1°