For the medal ceremony, a flagpole is set up on the field. From a point on the ground 12 m from its base, the angle of elevation to the top of the flagpole ...
Question 1 Report
For the medal ceremony, a flagpole is set up on the field. From a point on the ground 12 m from its base, the angle of elevation to the top of the flagpole is \(27^\circ\).
- Work out the height of the flagpole, correct to 3 significant figures. (2)
- Find the direct distance from the point on the ground up to the top of the flagpole, correct to 3 significant figures. (2)
- Sports day rules state that a ceremony flagpole must be at least 5.5 m tall. State whether this flagpole meets the rule. (1)
Answer Details
This question tests using the tangent ratio to find a height from an angle of elevation, then the cosine ratio to find the direct distance, and comparing the result with a stated rule.
- (a) [2] The height is opposite the \(27^\circ\) angle and the ground distance (\(12\) m) is adjacent to it: \[\text{height} = 12 \times \tan 27^\circ = 6.114\text{ m (3 s.f.)}\]
- (b) [2] The direct distance is the hypotenuse, with the ground distance adjacent to the angle: \[\text{distance} = \frac{12}{\cos 27^\circ} = 13.468\text{ m (3 s.f.)}\]
- (c) [1] Since the height, \(6.114\) m, is greater than the required \(5.5\) m, the flagpole does meet the rule.
Once the height is found using tangent, the direct distance can be found either with cosine (ground distance over direct distance) or with Pythagoras' theorem using the height and ground distance; both give the same result.
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