The Pythagorean Theorem in Three Dimensions Quick Check
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Question
A circus tent is in the shape of a square pyramid. Each edge of the square base is 20 m and its slant height is 13.5 m. Find the height of the tent. Round the answer to the nearest tenth.(1 point)
Responses
9.1 m
9.1 m
14.8 cm
14.8 cm
24.1 cm
24.1 cm
16.8 m
To find the height of the tent, we can use the Pythagorean theorem in 3 dimensions, which is:
\( h = \sqrt{s^2 - \left(\frac{s}{2}\right)^2} \)
Where h is the height, s is the slant height, and \( \frac{s}{2} \) is half of the base edge.
Plugging in the values, we get:
\( h = \sqrt{13.5^2 - \left(\frac{20}{2}\right)^2} = \sqrt{182.25 - 100} = \sqrt{82.25} ≈ 9.1 \text{ m} \)
Therefore, the height of the tent is approximately 9.1 meters.
The correct answer is: 9.1 m