Question

Round to the nearest integer as needed and look at photo for accurate description

Answer 1

We will have to use the Law of Sines, which states that:

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

Procedure:

0. We have to remember that the sum of the interior angles of a right triangle adds up to 180°. Then:

$A+B+C=180$

As we are given two angles, B and C, we can isolate for A:

$A=180-B-C$

Replacing the values we get:

$A=180-42-100$$A=38$

2. Now that we have the three angles, we can use the Law of Sines to get the sides:

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

Isolating for c:

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

Replacing the values:

$c=\frac{\sin 100}{\frac{\sin 42}{165}}$$c\approx243$

3. Finally, getting a also using the Law of Sines:

$a=\frac{\sin A}{\frac{\sin B}{b}}$

Replacing the values:

$a=\frac{\sin 38}{\frac{\sin 42}{165}}$$a\approx152$

Answer: A.

• A = 38°

,

• a = 152m

,

• c = 243m