Please help! A person standing 30 ft from a flagpole can see the top of the pole at a 35 degree angle of elevation. The person's
eye level is 5 ft from the ground. Fond the height of the flagpole.
1 answer:
Answer: The height of the pole is 26 ft
Step-by-step explanation: Please refer to the attached diagram for details.
The diagram shows a right angled triangle labeled PEG. The point P is the top of the flagpole, the point E is the eye level of the observer, while point G is the point where the flagpole touches the ground. However, we must not forget that the observer’s eye is 5 ft from the ground. This means the height of the flagpole in the triangle has an extra 5 ft that would be added after our calculation. So, we have an opposite, which is the unknown and an adjacent, which is the side that lies between the reference angle and the right angle (that is, 30). Also we have the reference angle as 35.
Using the trigonometric ratios,
TanE = opposite/adjacent
Tan35 = PG/30
By cross multiplication we now have
Tan35 x 30 = PG
0.7002 x30 = PG
21.006 = PG
The height of the pole is approximately 21 ft.
However, we remember that the eye of the observer is 5 ft away from the ground. That means the pole actually goes an additional 5ft when it touches the ground. Hence the actual length of the pole is 21 + 5 = 26
Height of pole = 26 ft
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