Question

As John walks 16 ft towards a chimney, the angle of elevation from his eye to the top of the chimney changes from 30° to 45°. Identify the height of the chimney from John's eye level to the top of the chimney rounded to the nearest foot.

Answer 1

ANSWER

The height is
`22ft`


Step-by-step explanation

Let the height of the chimney be x.


`\tan(45 \degree) = (x)/(y)`


`1 = (x)/(y)`


`x = y`


`\tan(30 \degree) = (x)/(16+ y)`


`( √(3) )/(3) = (x)/(16 + y)`

Cross multiply


`√(3) (16 + y) = 3x`


`16 √(3) + y √(3) = 3x`

Put


`y = x`

into the equation;


`16 √(3) + x √(3) = 3x`

Group similar terms:


`16 √(3)= 3x - x √(3)`


`16 √(3)= (3 - √(3))x`


`(16 √(3) )/(3 - √(3) ) = x`




`x=21.856`


The height of the chimney to the nearest feet is 22