Trigonometry

Geometry Level 2

At a point P the angle of elevation of the top of a hill is 36.3 degrees. At a point Q on the same horizontal line as P and the foot of the hill and 60.0 meters from P, the angle of elevation is 24.5 degrees. Find the height of the hill.

72.0 meters 69.0 meters 70.0 meters 71 meters

1 solution

Joram Otero
Jul 3, 2014

let x be the height of the hill
let y be the distance from the foot of the hill to the point P
let y + 60 be the distance from the foot of the hill to the point Q

$\tan { (36.3)=\frac { x }{ y } } \\ \tan { (24.5)=\frac { x }{ y+60 } }$

you can now solve for the x

$\frac { x }{ \tan { (36.3) } } =\frac { x }{ \tan { (24.5) } } -60\\ \\ x\quad =\quad 72.03$

Trigonometry

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