Question
Asked Sep 5, 2019
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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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Expert Answer

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.

 

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A Mountain 3.5 90 B 13 miles D

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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.

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A Mountain h 3.5 90 13 miles a tan9 Opposite Adjacent tan 9 h 0.1583 a a = -(1) 0.1583

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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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A Mountain 3.5 90 13 miles h tan 3.5° a 13 h 0.0612= a+13 On multiplying both sides by (a+13) 0.0612(a 13) h Dividing both sides by 0.0612 a13 0.0612 h in above equation Substituting 0.1583 h +13 = 0.0612 0.1583 h on both sides Subtracting 0.1583 h 13= 0.0612 0.1583 Taking h common on right side 1 13 h 1 0.0612 0.1583 13 h16.34-6.32] 13 h16.34-6.32] 13 h10.02 On dividing both sides by 10.02, we get 13 h 10.02 h 1.297 miles

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