Question

Given m angle A = 35°, and b = 4.2, find c. Show all work.

Answer 1

Answer:

$c=5.1\ units$

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the measure of angle B

we know that

In the right triangle ABC

$m\angle A+m\angle B=90^o$ ---> by complementary angles in a right triangle

we have

$m\angle A=35^o$

substitute

$35^o+m\angle B=90^o$

$m\angle B=90^o-35^o=55^o$

step 2

Find the length side c

Applying the law of sines

$\frac{c}{sin(C)}=\frac{b}{sin(B)}$

substitute the given values

$\frac{c}{sin(90^o)}=\frac{4.2}{sin(55^o)}$

$c=\frac{4.2}{sin(55^o)}=5.1\ units$