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Exam-Style Question on TrigonometryA mathematics exam-style question with a worked solution that can be revealed gradually |
Question id: 752. This question is similar to one that appeared on an IB AA Higher paper in 2024. The use of a calculator is allowed.
An astronaut measures the angle of elevation of a light on the surface of a mysterious sphere on a faraway planet.
The light is level with the centre of the sphere, so its distance above the ground is equal to the radius of the sphere.
The astronaut measures the angle to be 20°, and his theodolite is 15 metres away from the centre point where the sphere touches the ground. The theodolite is 1.7 metres tall.
(a) Calculate the radius of the sphere.
(b) Calculate the volume of the sphere.
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