Question

Looking out from his castle on the Isle of Misfit Toys, King Moonracer spots Santa's sleigh from a distance traveling toward the castle. The angle of elevation to Santa's sleigh is 20 degrees. Two minutes later, the angle of elevation is 52 degrees. How far did Santa travel and at what speed is he traveling, in miles per hour, if he is cruising at an altitude of 23,000 feet? Sketch a picture and show all your work.

Answer 1

WE have to calculate the base of the triangles:

Triangle 1 (black)

Apply the trigonometric function:

Tan θ = opposite side/adjacent side

Replacing:

Tan 20 =23,000 / x1

x1 = 23,000 /tan 20

x1= 63,192 feet

Triangle 2 (red)

x2= 23,000 /tan 50

x2= 19,300

Subtract 2x to x1

63,192-19,300 = 43,892 ft

Santa travelled 43,892 ft.

Speed = distance /time

Speed = 43,892 / 2 min = 21,946 miles per minute

S = 43,892 / 0.033333 hours = 1,316,760 miles per hout