General Sherman, a tree located in Sequoia National Park, stands 275 feet tall. To see the top of the tree, Carlos looks up at a 15° angle of elevation. If Carlos is 6 feet tall, how far is he from the base of the tree to the nearest foot?
Answers
Answer:
269 ft.
Step-by-step explanation:
The distance from the tree to Carlos is 1384 ft.
CD = Height of Carlos = 6 ft.
So,
AE = CD = 6 feet
EB = (AB - AE) = 275 - 6
= 269 ft.
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Answer:
Carlos is about 968 toes from the base of the tree to the nearest foot.
Step-by-step explanation:
We can use trigonometry to clear up this problem. Let x be the distance from Carlos to the base of the tree.
We understand that the tangent of an perspective is equal to the contrary aspect divided by way of the adjoining side. In this case, the contrary aspect is the peak of the tree (275 feet), and the adjoining facet is the distance from Carlos to the base of the tree (x + 6 feet, the place 6 toes is Carlos's height).
Therefore, we can write:
tan(15°) = 275 / (x + 6)
We can resolve for x by means of separating it on one facet of the equation:
x + 6 = 275 / tan(15°)
x = 275 / tan(15°) - 6
Using a calculator, we can discover that tan(15°) is about 0.268.
Plugging this price into the equation, we get:
x = 275 / 0.268 - 6
x ≈ 974 - 6
x ≈ 968
Therefore, Carlos is about 968 toes from the base of the tree to the nearest foot.
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