Question

Use the diagram of the right triangle above and round your answer to the nearest hundredth. If m Answer choices: A) 17.32 m
B) 6.83 m
C) 14 m
D) 9.99 m

Answer 1

If you use the law of sins, the answer would be B) 6.928 (in the law of sines you round so it would be 6.93)

Answer 2

Answer:

b. 6.93 m.

Step-by-step explanation:

We have been given triangle ABC and we are asked to find the measure of a.

We will use law of sines to solve our given problem.

$\frac{a}{\text{Sin}(A)}=\frac{b}{\text{Sin}(B)}=\frac{c}{\text{Sin}(C)}$, where a, b and c are opposite sides of angle A, B and C respectively.

First of all, we will find the measure of angle B using angle sum property.

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

$30^{\circ}+\angle B+90^{\circ}=180^{\circ}$

$\angle B+120^{\circ}=180^{\circ}$

$\angle B=180^{\circ}-120^{\circ}$

$\angle B=60^{\circ}$

Upon substituting our given values in law of sines we will get,

$\frac{a}{\text{Sin}(30^{\circ})}=\frac{12}{\text{Sin}(60^{\circ})}$

$\frac{a}{0.5}=\frac{12}{\frac{\sqrt{3}}{2}}$

$\frac{a}{0.5}=\frac{2*12}{\sqrt{3}}$

$\frac{a}{0.5}*0.5=\frac{24}{\sqrt{3}}*0.5$

$a=\frac{12}{\sqrt{3}}$

$a=6.9282032302755\approx 6.93$

Therefore, the value of a is 6.93 meters and option 'b' is the correct choice.