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?

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 =

⇒ AB = h &  B D = y + 700

⇒ Tan 22 =   ------------(1)

From triangle ABC

Tan 38 =

⇒ AB = h & BC = y

⇒ Tan 38 = ------------------(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.

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step-by-step explanation: