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klemol [59]
3 years ago
10

A campsite is 12.88 miles from a point directly below Mt. Adams. If the angle of elevation is 15.5° from the camp to the top of

the mountain, how high is the mountain?

Mathematics
1 answer:
nata0808 [166]3 years ago
4 0

Answer:

3.57 miles

Step-by-step explanation:

Please consider the attachment.

We have been given that a campsite is 12.88 miles from a point directly below Mt. Adams. The angle of elevation is 15.5° from the camp to the top of the mountain. We are asked to find the height of the mountain.

We can see from the attachment that h is opposite side to angle 15.5 degrees and 12.88 miles in adjacent side.

We know that tangent relates opposite side of right triangle with its adjacent side.

\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}

\text{tan}(15.5^{\circ})=\frac{h}{12.88}

\text{tan}(15.5^{\circ})\cdot(12.88)=\frac{h}{12.88}\cdot(12.88)

12.88\cdot\text{tan}(15.5^{\circ})=h

h=12.88\cdot\text{tan}(15.5^{\circ})

h=12.88\cdot(0.27732454406)

h=3.5719401274928

h\approx 3.57

Therefore, the mountain is approximately 3.57 miles high.

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