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Elan Coil [88]
3 years ago
9

A biker notices a mountain directly in front of her and determines that the angle of elevation to the summit is 3.5. After hikin

g 15 miles toward the mountain she records that the angle of elevation is 11. How tall is the mountain? Round the height to the nearest hundredth of a mile

Mathematics
1 answer:
OleMash [197]3 years ago
4 0

Answer:

The mountain is 1.34 miles tall.

Step-by-step explanation:

See the attached diagram.

The height of the mountain is h miles (say).

Now, from the right triangle Δ ABC,

\tan 3.5^{\circ} = \frac{AB}{AC} = \frac{h}{x + 15}

⇒ x + 15 = \frac{h}{\tan 3.5^{\circ}} = 16.35h ........... (1)

Again, from the right triangle Δ ABD,

\tan 11^{\circ} = \frac{AB}{AD} = \frac{h}{x}

⇒ x = \frac{h}{\tan 11^{\circ}} = 5.14h ............. (2)

Now, solving equations (1) and (2) we get,

15 = (16.35 - 5.14)h = 11.2h

⇒ h = 1.34 miles (To the nearest hundredth of a mile)

Therefore, the mountain is 1.34 miles tall. (Answer)

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