Question

Tony is standing at sea level. From his location, the angle of elevation of the top of Blue Mountain is 25°. Staying at sea level, he walks 200 yards toward the mountain. The angle of elevation of the top is now 30°. Find the height of Blue Mountain. Round intermediate results to 3 decimal places and the final answer to 1 decimal place.

The height of Blue Mountain is ____ yards

Answer 1

h = 1558.8

Explanation:

Let x be the distance from the vertex of the 30 degree angle to the base of Blue mountain.

Tan (30) = h/x Multiply both sides by x.

x * Tan(30) = h

Tan(25) = h/(x + 200) Multiply x + 200 on both sides.

(x + 200) * Tan(25) = h

Now you have 2 equations both equal to h. The two sides can be equated to each other.

x*tan(30) = (x + h) * Tan(25) Divide both sides by tan(25)

x*tan(30)/tan(25) = x + 200 Find Tan(30)/Tan(25)

Tan30 / tan(25) = 1.23813 so

1.23813 x = x + 200 Subtract x from both sides.

0.23813x = 200 Divide both sides by 0.23813

x = 200/0.23813

x = 839.99

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That is not the answer you have been asked for. What you need is h.

Tan(30) = x / h Multiply both sides by h

h*tan(30) = x Divide both sides by tan(30)

h = x/tan(30)

h = 839.99/tan(30) Tan 30 = 0.57735

h = 839.99/0.57735

h = 1558.8