A falcon flying at a height of 200 yards spots a sparrow flying at a height of 150 yards. The location of the sparrow makes an angle of 40° from the horizontal line through the falcon's location. What is the distance x between the falcon and the sparrow? Assume that the ground beneath the birds is level.

Question

Mathematics

Zachery Coffey

8 October, 08:39

A falcon flying at a height of 200 yards spots a sparrow flying at a height of 150 yards. The location of the sparrow makes an angle of 40° from the horizontal line through the falcon's location. What is the distance x between the falcon and the sparrow? Assume that the ground beneath the birds is level.

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Answers (1)

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Nathan Smith · Answer 1

The difference of the heights of the falcon and the sparrow:

200 - 150 = 50 yards

sin 40° = 50 / x

x = 50 / sin 40°

x = 50 / 0.6428

x = 77.8 ≈ 78 yd

Answer:

The distance between the falcon and the sparrow is D) 78 yards.