Question

Two kites are stuck on the same spot on a tree. The angle of elevation of kite 1 to the tree from the ground at point A is 53° . If the length of the kite 2 string from the ground (say point B ) is 12 root 2 ft , find theta if given AB = 3 ft.​

Answer 1

Given:

Two kites are stuck on the same spot on a tree.

The angle of elevation of kite 1 to the tree from the ground at point A is 53° .

The length of the kite 2 string from the ground (say point B ) is 12 root 2 ft.

To find:

The angle theta if given AB = 3 ft.​

Solution:

Consider the attached figure, while going through the following steps.

From figure it's clear that,

cos ∅ = AB / 12√2

⇒ cos ∅ = 3 / 12√2

⇒ cos ∅ = 1 / 4√2

⇒ cos ∅ = 0.17677

⇒ ∅ = cos^-1  (0.17677)

∴ ∅ = 79.81°