Let Δ ABC be a triangle whose area is 10 \sqrt3 units with side length |AB| = 8 units and |AC| = 5 units. Find possible values of the angle A.

Correct Answer is : 60° or 120°

NIMCET 2013 Question Paper with solutions

Question : 7 of 120

Marks: +1, -0

Let Δ ABC be a triangle whose area is 10

√3

units with side length |AB| = 8 units and |AC| = 5 units. Find possible values of the angle A.

Solution:

Given, area of triangle

=10√3

⇒10√3+1/2×ab×\sinθ

[∵area of triangle

=1/2ab\sinθ

]

⇒10√{3}=\;\;{1}/{2}×8×5\sinθ

⇒\sinθ=\;\;{10√{3}×2}/{8×5}

⇒\sinθ=\;\;{2√{3}}/{4}=\;\;{√{3}}/{2}

⇒\sinθ=\;\;{√{3}}/{2}⇒θ=60^{∘}

or 120°

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