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Marrero is in a hot-air balloon that is 600 feet above the ground, where he can see two people.

b. If the angle of depression from his line of sight to the person at C is 20˚, how far is the person from the point on the ground below the hot-air balloon?


Round your answer to the nearest feet (whole number).



User Soccerlife
by
7.1k points

1 Answer

5 votes

Answer: The distance from the person on the ground to the bottom of the hotair balloon is 1,649 ft

Step-by-step explanation: Please refer to the attached diagram

From the diagram, the hotair balloon is labelled B. If Marero looks down and forms an angle of depression of 20°, that means he is forming an angle of 70° to point C where one of the two persons are standing. Point B is an angle of 70° (point A cuts point B at a perpendicular, that is, 90°)

With these we can now use the trigonometrical ratio of tangent to calculate the distance marked x on the diagram.

Tan B = opposite/adjacent

Tan 70 = x/600

When we cross multiply, we now have

Tan 70 × 600 = x

2.7475 × 600 = x

1648.5 = x

Rounded to the nearest feet

x = 1,649 feet

Marrero is in a hot-air balloon that is 600 feet above the ground, where he can see-example-1
User Sumit Ramteke
by
6.3k points
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