Question

Find the other two sides of triangle having angles 30°,30°, 120° if the largest side 6m is in metres

Answer 1

The other two sides of the triangle are 2√3 m

Explanation:

The figure is attached

The given triangle is ABC where the angles are shown

Side BC will be the largest because it is opposite to the largest angle of the triangle

The triangle ABC will be isosceles

Drawing perpendicular AD from A on BC

∵ ABC is an isosceles triangle

And, AD ⊥ BC

∴ BD = DC = 3 m

In Right angled ΔABD

$\cos 30^\circ = \frac{BD}{AB}$

$\implies \frac{\sqrt{3}}{2}=\frac{3}{AB}$

$\implies AB=\frac{6}{\sqrt{3}}$

$\implies AB=2\sqrt{3}$ m

∵ AB = AC    (Isosceles Triangle)

∴ AC = 2√3 m

Therefore, the other two sides of the triangle are 2√3 m

Hope this answer is helpful.

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