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Refer to the above figure and find the length of $AC$ , if the area of triangle $ABC$ is $15$ .

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9.2

7.2

6.2

8.2

answer is C.

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Detailed Solution

It is given that area of the triangle ABC is 15 sq. units.
Question Image

By sine rule, we get

\frac{AC}{\sin 52} = \frac{CB}{\sin 38}

\Rightarrow CB = 0.7813 AC

Area of triangle is

\frac{1}{2} \times AC \times CB

.
Substitute the value of BC.

= 0.39 {AC}^{2} = 15

\Rightarrow {AC}^{2} = 38.46

\Rightarrow AC = 6.2

Hence, the correct option is (3).

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