Question

An airplane over the Pacific Ocean sights an atoll at an 7° angle of depression. If the plane is 663 m above the water, how many kilometers is it from a point 663 m directly above the atoll?(Hint: Make sure your calculator is in degrees!)
A. 5399.7 km
B. 5.4 km
C. 81.41 km
D. 760.8 km

Answer 1

You need to draw the diagram to understand the problem easily. Teh diagram will show the right triangle, acute angle with the base  7º, height is 663 m, and "x" is the base of the triangle. 

using the tangent ratio: 

tanΘ = opposite / adjacent

tan7º = 663 m / x 

x = 663 m / tan7º
x = 5,399.7 m 

change m to km. 1,000 m = 1km

5,399.7m * 1km/1,000 m = 5,399.7 km/1000 = 5.3997 km or 5.4 km

B. 5.4 km