Question

Hector is flying a kite. He has let out 86 feet

of string and is holding it 4 feet off the
ground. If the string is at an angle of
elevation of 42°15’30”, how high is the kite?

Answer 1

Hector's kite is 61.84 feet from the ground.

Explanation:

The angle of elevation of the kite is 42°15’30” when converted to decimals, it is
`42.258333^(0)` ≅
`42.26^(0)`

Let the height of the kite to the horizontal of angle of elevation be represented as x. Applying the trigonometric function to the sketch of Hector's kite,

Sin θ =
`(opposite)/(hypotenus)`

Sin
`42.26^(0)` =
`(x)/(86)`

⇒ x = 86 x Sin
`42.26^(0)`

= 86 x 0.6725

= 57.835

x ≅ 57.84 feet

The height of Hector's kite from the ground = x + 4

= 57.84 + 4

= 61.84 feet