Question of The Day07-06-2021

Point A and B are on the opposite side of the hill and were 48 m and 12 m away from the foot of the hill respectively. The angle of elevation from Point A to the peak of the hill is complementary to the angle of elevation from point B to the peak of the hill. What is the height of the hill?

Correct Answer : c ) 24 m

Explanation :

According to the question

Let ∠DBA = θ and AD is the height of the Hill

A and B are on the opposite side of the Hill and were 48 m and 12 m respectively

Angle of elevation to the top of the hill to the point A and B is complementary

We know that two angles are complementary to each other if the sum is 90⁰.

⇒∠DBA = θ , ∠DCA = (90 – θ)

We know that

tanθ=$$p \over b$$

Where p is the perpendicular and b is the base of the triangle

In △ABD

tanθ=$$AD \over BD$$

Substituting the values

tanθ=$$AD \over 48$$……..(1)

tan(90-θ)=$$AD \over 12$$

We know that

tan(90 – θ) = cot θ

cotθ=$$1 \over \tan\ θ$$

⇒cotθ=$$AD \over 12$$

⇒tanθ=$$12 \over AD$$…….(2)

comparing equation (1) and (2)

$${AD \over 48}$$=$${12 \over AD}$$

⇒AD=$$\sqrt {576}$$