Question

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

Answer 1

Answer:

Option D is correct.

Step-by-step explanation:

Given,

In ΔABC, ∠A = 42° , ∠B = 56° & a = 7

We use law of sines,

which has following expression:

$\frac{a}{sin\,A}=\frac{b}{sin\,B}\frac{c}{sin\,C}$

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

$\frac{7}{sin\,42}=\frac{b}{sin\,56}$

$\frac{7}{0.67}=\frac{b}{0.83}$

$b=\frac{7}{0.67}\times0.83$

$b=8.67$

$\frac{7}{sin\,42}=\frac{c}{sin\,82}$

$\frac{7}{0.67}=\frac{c}{0.99}$

$c=\frac{7}{0.67}\times0.99$

$c=10.36$

Therefore, Option D is correct.