Question

Three points on the ground form an equilateral triangle. There is a vertical pillar at
A
. The angle of elevation of the top of the pillar is 53° from the midpoint of BC and theta° from the midpoint of AB. Find tan theta

Answer 1

Given:

Three points on the ground form an equilateral triangle.

Points be A, B and C.

There is a vertical pillar at  A.

The angle of elevation of the top of the pillar is 53° from the midpoint of BC.

The angle of elevation of the top of the pillar is Ф° from the midpoint of AB.

To Find:

tan Ф

Solution:

Let D be the mid point of BC.

E be the midpoint of AB.

Let Q be the top point of the pillar.

If m is the altitude of the triangle ΔABC ,

• m = AD
• m =√ a² - (a/2)² = a√3/2

Consider ΔDAQ,

• tan 53° = AQ/AD = h/m = 2h/a√3
• 2h/a√3 = 4/3
• h = 2a/√3

Now consider ΔEAQ,

• tan Ф = h/AE = (2a/√3)/ a/2 = 4/√3

Therefore,

The value of tan Ф = 4/√3.