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Distance from home to store = 4 * 0.5 = 2 miles.
Time taken to return home = (2/12) * 60 =10 minutes.
Total distance traveled = 2 * 2 = 4 miles.
Total time taken = 30 + 10 = 40 minutes.
Average speed for entire trip = total distance / total time in hours.
Time taken to return home = (2/12) * 60 =10 minutes.
Total distance traveled = 2 * 2 = 4 miles.
Total time taken = 30 + 10 = 40 minutes.
Average speed for entire trip = total distance / total time in hours.
The height of the smaller building is <u>94.63 feet</u>, computed using the trigonometric ratios.
In the question, we take AB to be the taller building, where A is its top and B is its base, CD to be the shorter building, where C is its top and D is its base, and CE to be the perpendicular from C to AB.
Given that the horizontal distance between the two buildings is 260 feet, we can say that BC = CE = 260 feet.
The angle of elevation from the top of the shorter building to the top of the taller building is 30°, that is, ∠ECA = 30°.
The angle of depression from the top of the shorter building to the base of the taller building is 20°, that is, ∠ECB = 20°.
When ∠ECB = 20°, then ∠CBD = 20°, as they are alternate angles.
We are asked to find the height of the shorter building, that is, we are asked to find CD.
In ΔCBD,
tan ∠CBD = CD/BD {perpendicular/base},
or, tan 20° = CD/260,
or, CD = 260*tan 20° = 260*0.36397023426 {∵ tan 20° = 0.36397023426},
or, CD = 94.6322609092.
Therefore, the height of the smaller building is <u>94.63 feet</u>, computed using the trigonometric ratios.
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