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DerKrebs [107]
3 years ago
5

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

Mathematics
2 answers:
Ivenika [448]3 years ago
7 0
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)
grandymaker [24]3 years ago
7 0

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.

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