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Question

The area of a triangle is 12 sq. cm. Two sides are 6 cm and 12 cm. The included angle is

A
cos1(13)
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B
cos1(16)
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C
sin1(16)
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D
sin1(13)
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Solution

The correct option is C sin1(13)
Consider the given triangle

Let a=6cm and b=12cm

Therefore the included angle is θ=C

area=(height)(base)2

area=bh2

now h=asinθ

therefore

area=basinθ2

12=(12)(6)sinθ2

sinC=sinθ=13

Hence C=θ=sin1(13)

The answer is D

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