Question 15
Bret is standing 75.15 meters from a hot air balloon that is
preparing to take off. The angle of elevation from Bret to
the top of the balloon is 37 degrees. Find the height of the
balloon. Round your answer to the nearest hundredth if
necessary.
Height of the balloon meters
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Question 15
Bret is standing 75.15 meters from a hot air balloon that is
preparing to take off. The angle of elevation from Bret to
the top of the balloon is 37 degrees. Find the height of the
balloon. Round your answer to the nearest hundredth if
necessary.
Height of the balloon

meters
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UpStudy AI · Accepted Answer

1. We are given that Bret is standing $$75.15$$ meters from the balloon and the angle of elevation is $$37^\circ$$.

2. In the right triangle formed, the tangent of the angle relates the opposite side (height of the balloon, $$h$$) to the adjacent side (distance from Bret, $$75.15$$ m):
   $$
   \tan(37^\circ) = \frac{h}{75.15}
   $$

3. Solve for $$h$$ by multiplying both sides by $$75.15$$:
   $$
   h = 75.15 \cdot \tan(37^\circ)
   $$

4. Using a calculator, compute $$\tan(37^\circ)$$. We find:
   $$
   \tan(37^\circ) \approx 0.75355
   $$

5. Multiply to find the height:
   $$
   h \approx 75.15 \times 0.75355 \approx 56.63
   $$

6. Therefore, the height of the balloon is approximately:
   $$
   \boxed{56.63 \text{ meters}}
   $$
The height of the balloon is approximately 56.63 meters.

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