Question

A 6 ft. tall man flies a kite and lets out 100 feet of string. The angle of elevation of the string is 52° . How high off the ground is the kite?

Answer 1

here we are given that a 6ft high man is flying a kite with a string of length 100ft at an angle of elevation 52° . We would like to calculate the height of the kite above the ground. For figure refer to the attachment. We would have to make use of trigonometric ratios here as ,

In ∆ ABE ,

`\longrightarrow \sin 52^o = (AB)/(AE) \\`

`\longrightarrow 0.8 =(y)/(100ft) \\`

`\longrightarrow y =0.8(100ft) \\`

`\longrightarrow y = 80ft \\`

Now the total height above the ground will be ,

`\longrightarrow h = y + h_(man) \\`

`\longrightarrow h = (80 + 6)ft\\`

`\longrightarrow\underline{\underline{ h = 86\ ft. }} \\`

And we are done!