Answer:
The height of the hill = h = 580.7 feet
Step-by-step explanation:
Let height of the hill = h
From the triangle A B D
Tan 22 = [tex]\frac{AB}{BD}[/tex]
⇒ AB = h & B D = y + 700
⇒ Tan 22 = [tex]\frac{h}{y + 700}[/tex] ------------(1)
From triangle ABC
Tan 38 = [tex]\frac{AB}{BC}[/tex]
⇒ AB = h & BC = y
⇒ Tan 38 = [tex]\frac{h}{y}[/tex] ------------------(2)
⇒ h = y tan 38 -----------------(3)
Put the value of h from equation (3) into equation (1) we get
⇒ (tan 22) × (y + 700) = y × tan 38
⇒ 0.40 y + 282.82 = y × 0.78
⇒ y = 742.12 feet -----------------(4)
Put this value of y in equation 3 we get
⇒ h = 742.12 × tan 38
⇒ h = 580.7 feet
This is the height of the hill.
