Question

Use the diagram of the right triangle above and round your answer to the nearest hundredth.

Answer 1

Option a: $17.32 \ {m}$ is the length of b

Explanation:

The angle of B is $\angle B=60^{\circ}$ and $a=10 \ m$

We need to determine the length of b.

First, let us determine the angle of A.

Since, ABC is a triangle, then all the angles add up to 180°

Thus, we have,

$\angle A+\angle B+\angle C=180^{\circ}$

$\angle A+60^{\circ}+90^{\circ}=180^{\circ}$

       $\angle A+150^{\circ}=180^{\circ}$

                   $\angle A=30^{\circ}$

Thus, the angle of A is $\angle A=30^{\circ}$

Now, we shall determine the length of b using the sine law formula.

The formula for sine law is given by,

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

where $a=10 \ m$ , $\angle A=30^{\circ}$ , $\angle B=60^{\circ}$

Thus, we have,

$\frac{10}{\sin 30}=\frac{b}{\sin 60}$

Simplifying, we get,

$\frac{10}{0.5}=\frac{b}{0.866}$

Multiplying both sides by 0.866, we get,

$\frac{10\times0.866}{0.5}=b$

Multiplying the numerator, we have,

$\frac{8.66}{0.5}=b$

Dividing, we get,

$17.32=b$

Thus, the length of b is $b=17.32 \ m$

Hence, Option a is the correct answer.