Question #268719

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.


1
Expert's answer
2021-11-23T08:51:36-0500



Find the length of hypotenuse y

Using sine rule


asinA=bsinB=csinC\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}


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


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


y=82.36my=82.36m


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

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


h=82.36×sin(37.93°)h=82.36\times sin(37.93\degree)


h=50.63mh=50.63m


height of the hill is 50.63meters




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