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:

• ABC form an equilateral triangle.
• The angle of elevation of the top of the pillar at A is 53° from the midpoint of BC
• The angle of elevation of the top of the pillar at A is Ф from the midpoint of AB

To find:

tanФ

Answer:

• Let each side of ΔABC be x units, the midpoint of AB be D and of BC be E.
• Let the top of pillar be represented by O.
• ∵ΔABC is equilateral, AE = √3x/2

In ΔOAE,

• tan 53° = OA/AE
• 1.327 = 2OA/(√3x)
• OA = 1.15x

In ΔOAD,

• tanФ = OA/AD
• tanФ = 1.15x/(x/2) = 2.3

tanФ = 2.3