Answer in Trigonometry for seiji #268719
October 16th, 2022
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.
Find the length of hypotenuse y
Using sine rule
“frac{a}{sinA}=frac{b}{sinB}=frac{c}{sinC}”
“frac{y}{sin(22.61degree)}=frac{56.6}{sin(15.32degree)}”
“y=frac{56.6times sin(22.61degree)}{sin(15.32degree)}”
“y=82.36m”
Now we have the Hypotenuse Y lets find the height h of the hill
“sintheta=frac{opposite(h)}{Hypotenuse(y)}”
“h=82.36times sin(37.93degree)”
“h=50.63m”
height of the hill is 50.63meters
