Question

Given a possible triangle abc with a=16, b=25 a=22 find a possible value for b round to the nearest tenth.

a. 29.7°
b. 35.8°
c. 139.0°
d. no solution

Answer 1

b.35.8°

Explanation:

Given: We are given two sides and an angle.

a = 16, b = 25 and ∠A = 22°

We have to find the ∠B.

Here we can use sine formula and find the value of the ∠B

`(sin A)/(a ) = (sin B)/(b)`

Now plug in the given values, we get

`(sin 22)/(16) = (sin B)/(25)`

Use calculator and find the value of sin 22 = 0.37

0.37/16 =sinB/25

cross multiplying, we get

0.37*25 = 16 sin B

9.25 = 16 sin B

sin B = 9.25/16

sin B = 0.58

B =
`sin^(-1) (0.58)`

B = 35.8°

So the answer is b. 35.8°

Answer 2

We can use the Sine Law:
a / sin A = b / sin B
16 / sin 22° = 25 / sin B
16 / 0.3746 = 25 / sin B
sin B = 25 · 0.3746 / 16
sin B = 0.5853
∠B = sin^(-1) 0.5853
∠B = 35.83° ≈ 35.8°
Answer: b. 35.8°