Question

A hiker approximates an angle of elevation to the top of a hill to be 22 degrees. After walking 700 feet closer, the hiker notices the angle of elevation has increased by 16 degrees. How high is the hill?​

Answer 1

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 = $\frac{AB}{BD}$

⇒ AB = h &  B D = y + 700

⇒ Tan 22 =  $\frac{h}{y + 700}$ ------------(1)

From triangle ABC

Tan 38 = $\frac{AB}{BC}$

⇒ AB = h & BC = y

⇒ Tan 38 = $\frac{h}{y}$ ------------------(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.