Question

In the triangle below, b =________. If necessary, round your answer to two

decimal places.
A
42°
C
Answer here
B
41.5%
37

Answer 1

b ≈ 54.94

Explanation:

using the Sine rule in Δ ABC

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

where a is the side opposite ∠ A, b is opposite ∠ B , c is opposite ∠ C

we require to calculate ∠ B

∠ B = 180° - (42 + 41.5)° = 180° - 83.5° = 96.5°

to find b using the pair of ratios

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

`(b)/(sin96.5)` =
`(37)/(sin42)` ( cross- multiply )

b × sin42° = 37 × sin96.5° ( divide both sides by sin42° )

b =
`(37sin96.5)/(sin42)` ≈ 54.94 ( to 2 decimal places )