Question

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 falcons location. What is that distance x between the falcon and the sparrow? Assume that the ground beneath the bird is level.

Answer 1

Answer:78

Explanation:

Answer 2

Answer: The distance between the birds is about 77.78 yards.

This is a trigonometry problems, so it helps to draw a right triangle between the birds. The length between them is the hypotenuse and we have a angle of 40 degrees by the sparrow. The side opposite the sparrow is the difference in heights of the birds, 50 yards.

Therefore, we can write and solve the following sine relationship.

sin(40) = 50/x
0.6428 = 50/x
x = 77.78