Question

Given that A = 42°, B = 56°, and a = 7, solve triangle ABC. Round the answers to the nearest hundredth, if necessary.

A. C=82°, b=3.92, c=10.36

B. C=2°, b=3.92, c=10.36

C. C=2°, b=8.67, c=10.36

D. C=82°, b=8.67, c=10.36

Answer 1

Option D is correct.

Explanation:

Given,

In ΔABC, ∠A = 42° , ∠B = 56° & a = 7

We use law of sines,

which has following expression:

`(a)/(sin\,A)=(b)/(sin\,B)(c)/(sin\,C)`

First we find value of ∠C

∠A + ∠B + ∠C = 180° (Angle Sum Property of Triangle)

42 + 56 + ∠C = 180

∠C = 180 - 98

∠C = 82°

Now using law of sines, we get

`(7)/(sin\,42)=(b)/(sin\,56)`

`(7)/(0.67)=(b)/(0.83)`

`b=(7)/(0.67)*0.83`

`b=8.67`

`(7)/(sin\,42)=(c)/(sin\,82)`

`(7)/(0.67)=(c)/(0.99)`

`c=(7)/(0.67)*0.99`

`c=10.36`

Therefore, Option D is correct.