QuestionA building casts a 130 ft shadow with the Sun at an $82.9^{\circ}$ angle. Find the building's height.

Studdy Solution

STEP 1

Question: What does the angle formed by the Sun's rays with the Earth represent in the right triangle formed by the building, its shadow, and the Sun's rays?
A) The angle opposite to the side representing the building's height B) The angle opposite to the side representing the shadow C) The angle at the vertex representing the top of the building D) The angle at the vertex representing the end of the shadow
Answer: A

STEP 2

Question: Which trigonometric function relates the angle formed by the Sun's rays with the Earth, the building's height, and the length of the shadow?
A) Sine B) Cosine C) Tangent D) Cotangent
Answer: C

STEP 3

Question: How can we rearrange the formula $\tan(\theta) = \frac{Height}{Shadow\, length}$ to solve for the building's height?
A) $Height = \tan(\theta) \times Shadow\, length$ B) $Height = \frac{\tan(\theta)}{Shadow\, length}$ C) $Height = \frac{Shadow\, length}{\tan(\theta)}$ D) $Height = \tan(\theta) + Shadow\, length$
Answer: A

STEP 4

Question: If $\theta = 82.9^{\circ}$ and $Shadow\, length = 130$ feet, how can we calculate the building's height using the formula from the previous question?
A) $Height = \tan(82.9^{\circ}) \times 130$ feet B) $Height = \tan(130) \times 82.9$ feet C) $Height = \tan(82.9^{\circ}) + 130$ feet D) $Height = \tan(130) + 82.9$ feet
Answer: A

STEP 5

Question: If $\tan(82.9^{\circ}) \approx 7.115369722$ , what is the approximate height of the building?
A) 924.9980628 feet B) 1075.9980628 feet C) 850.9980628 feet D) 1000.9980628 feet
Answer: A

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