Answer to Question #268719 in Trigonometry for seiji

Question

At point P, the angle of elevation of the top of a hill is 37.93°. At point Q on the same horizontal line as P and the foot of the hill and 56.6 meters from P, the angle of elevation is 22.61°. Find the height of the hill.

Answer 1

Find the length of hypotenuse y

Using sine rule

$\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}$

$\frac{y}{sin(22.61\degree)}=\frac{56.6}{sin(15.32\degree)}$

$y=\frac{56.6\times sin(22.61\degree)}{sin(15.32\degree)}$

$y=82.36m$

Now we have the Hypotenuse Y lets find the height h of the hill

$sin\theta=\frac{opposite(h)}{Hypotenuse(y)}$

$h=82.36\times sin(37.93\degree)$

$h=50.63m$

height of the hill is 50.63meters