Geometry and TrigonometryMediumDistance from a building using a 45° angle
Geometry and Trigonometry practice question
From a point on level ground, the angle of elevation to the top of a 30-metre tower is 45°. How many metres is the point from the base of the tower?
Answer: 30
tan 45° = height/distance = 1, so the distance equals the height: 30 metres.
Common wrong answers
- If you answered 15
- 15 halves the height; a 45° angle makes the two legs equal.
- If you answered 60
- 60 doubles the height.
- If you answered 42.4
- 42.4 is 30√2, the distance to the TOP of the tower (the hypotenuse), not to the base.
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