A tower that is 65m high makes an obtuse angle with the ground. The vertical distance from the top of the tower to the ground is 59m.

Question

What obtuse angle does the tower make with the ground, to the nearest hundredth of a radian? (continuation of the question)

For this question I sketched the triangle and solved by using sin and got an answer of 1.1377, which is correct. But after you had to subtract pi from that answer, and I was confused on to why you had to do that, can someone explain? Thanks.

Answer 1

If the tower makes an obtuse angle, it also makes an acute angle with the ground

sin^-1(59/65) = sin^1(.907) = 65.2 degrees = .346pi radians = .346(3.14159) = 1.087 radians

less than pi/2 radians is an acute angle pi/2 = 1.57 radians

about 1.1 radians is the acute angle, subtract it from pi radians to get the obtuse angle. The obtuse + acute angle = pi radians

3.14159 - 1.087 = 2.055 radians = the obtuse angle

which also = 2.055/3.14159 = 0.654 pi radians

the tower leans away from the ground from one side, but towards the ground on the other side, so it forms an obtuse and an acute angle, which sum to pi radians

Answer 2

What you found was the acute angle. The problem is wanting the obtuse angle on the other side of the tower.

Since the two angles are supplementary, to get the obtuse angle, subtract what you found from pi.

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59| \ 65

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|_a\x_______

You found a, x = pi - a