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 falcon's location. What is the distance x between the falcon and the sparrow? Assume that the ground beneath the birds is level.

Answer 1

See attached for diagram drawn

Find the difference in the height between the falcon and the sparrow:

200 - 150 = 50 m

Find the distance between the the falcon and the sparrow:

Let x be the distance.

The distance will be the hypotenuse between the two birds.

sin θ = opp/hyp

sin 40º = 50 / x

x = 50/sin 40º

x = 77.79 yard

Answer: The distance between them is 77.79 yard