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

Question

asked Mar 18, 2019 64.7k views

2 Answers

Josh Stone · Answer 1 · 2019-03-23T13:13:41+0000

Answer:

b. 6.93 m.

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,

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

(a)/(0.5)=(12)/((√(3))/(2))

(a)/(0.5)=(2*12)/(√(3))

(a)/(0.5)*0.5=(24)/(√(3))*0.5

a=(12)/(√(3))

$a=6.9282032302755\approx 6.93$

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