# In travelling across flat land, you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5 degrees. After you drive x=13 miles closer to the mountain, the angle of elevation is 9 degrees. Approximate the height of the mountain.

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In travelling across flat land, you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5 degrees. After you drive x=13 miles closer to the mountain, the angle of elevation is 9 degrees. Approximate the height of the mountain.

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Step 1

First we would draw the diagram of the given situation on the board.

According to figure, AB or h is the height of the mountain. C is my initial position and D is final position.

Step 2

First we will take triangle ABD and will apply tangent ratio.

After applying tangent ratio, we will solve the equaiton for a in terms of h.

We got a= h/0.1583.

Step 3

Now in triangle ABC, we will apply tangent ratio.

Then we will substitute value of a that is a = h/ 0.1583 and solve for h.

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