Kelsey belongs to a rocket club and has made a new model rocket. She wants to launch it and calculate the height of it, but on launch day it is quite windy. She has built a devices that measures the angle of elevation as the rocket sis on the ground. Her friend Holly also has this same style of device and will assist Kelsey in measure the height of her rocket from a second position. Kelsey is positioned 125 feet upwind of the launch pad and records her rocket a 67 degrees. Holly is 150 downwind and records an angle of elevation for Kelsey's rocket at 72 degrees. How high did the rocket go? Hint: Where will the rocket go if the wind is blowing?
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The total distance between Holly and Kelsey is 150 + 125 = 275 ft.
Assume distance between Holly and rocket at its apex is x1, then x2 = 275 - x1.
tan(67)*(275 - x1) = tan(72)*(275 - x2); doing a little algebra:
3.078x2 - 2.356x1 = 198.50 (equation I)
tan(67) = h / x2, h = tan(67)*x2 (where 'h' is height of rocket).
tan(72) = h / x1, h = tan(72)*x1
tan(72)*x1 = tan(67)*x2
3.0777x1 = 2.3559x2
x1 = 2.3559x2 / 3.0777
x1 = 0.7655; substitute 0.7655 for x1 in equation I
3.078x2 - 2.356(0.7655) = 198.50
x2 = 155.725
since: tan(67) = h / x2
2.356 = h / 155.725
h (height of rocket) = 367 feet
Assume distance between Holly and rocket at its apex is x1, then x2 = 275 - x1.
tan(67)*(275 - x1) = tan(72)*(275 - x2); doing a little algebra:
3.078x2 - 2.356x1 = 198.50 (equation I)
tan(67) = h / x2, h = tan(67)*x2 (where 'h' is height of rocket).
tan(72) = h / x1, h = tan(72)*x1
tan(72)*x1 = tan(67)*x2
3.0777x1 = 2.3559x2
x1 = 2.3559x2 / 3.0777
x1 = 0.7655; substitute 0.7655 for x1 in equation I
3.078x2 - 2.356(0.7655) = 198.50
x2 = 155.725
since: tan(67) = h / x2
2.356 = h / 155.725
h (height of rocket) = 367 feet