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

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.