A surveyor is trying to measure the height of a tree using a laser rangefinder,

Question

A surveyor is trying to measure the height of a tree using a laser rangefinder, which will give the distance from the device up to a distant object. The rangefinder stays at a fixed location, on a tripod 1m above the ground and is allowed to spin. The surveyor first points at the tree with the laser beam parallel to the ground and he determines that he is 40 meters away from it. He then spins the rangefinder, points to the treetop and determines it is 50 meters away from his device. (Let's assume all quantities are exact, for simplicity) a) What is the height of the tree? b) How many degrees did he spin the rangefinder to measure the distance to the treetop?

Explanation / Answer

A) height of the tree = sqrt(50^2 - 40^2) + 1

= 31 m answer

B) angle = arccos (40/50)

= 36.9 degree answer

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