Question

Suppose a ski jumper is 2,650 feet from the base of a ski jump and looks up to the top at an angle of elevation of 26 degrees. Approximately how high is the ski jump? Round your answer to the nearest whole foot.

Answer 1

We can draw a right triangle to easily visualize the given problem. Since the ski jumper is 2650 ft from the base of the ski jump, we can consider this as one of the right triangle's legs.

What we're looking for is the height of the ski jump or the other leg of the right triangle. Since the ski jumper looks up at an angle of elevation of 26°, we can use the tangent function to find the missing height. You may refer to the image below to better understand the problem.

Recall that tanθ = (opposite side facing the angle)/(side adjacent to the angle). For this case, we have


`\tan26= (x)/(2650)\\2650(\tan26) = x\\x \approx1292.49`

Hence, the height of the ski jump (rounded off the nearest whole foot) is 1292 feet.

Answer: 1292 feet