Initial angle of elevation is 30° and hypotenuse = 180 feet.
Since the angle that the building makes with the ground is 90°, therefore, it forms a 30-60-90 triangle.
In such a triangle, the sides are in the ratio 1: √3 : 2
Thus, hypotenuse = 180 feet (given), height of building = 90 feet and base = 90√3 feet.
Now, let's jump into the statements -
STATEMENT 1: After the movement, the elevation angle of the crane's arm is 60°.
We know that the angle the building makes with the ground is 90 and another angle is 60, so it is again a 30-60-90 triangle, we can easily determine the base of this triangle by using the formula: tan 60 = perpendicular / base (here, perpendicular = height of building = 90 feet)
Sufficient AD
STATEMENT 2: After the movement, the crane is at a distance of 30√3 feet from the building.
We already know the distance of the crane from the building at 30° elevation. This statement gives the current distance from the building. Subtracting the two will give us the distance the crane has moved.
SufficientTherefore, answer is (D)Bunuel wrote:
A crane is trying to reach the ninth floor of an under-construction multi-storey building. The length of the crane’s arm is flexible and can be increased or decreased. To reach the ninth floor, the crane raises its arm at an elevation angle of 30o and the arm length is 180 feet. The crane then moves closer to the building to reach the same floor at a different elevation angle. How much distance did the crane move? Assume the crane’s height to be negligible.
(1) After the movement, the elevation angle of the crane's arm is 60°.
(2) After the movement, the crane is at a distance of 30√3 feet from the building.
Project PS Butler
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