Higher January 2022 Paper 2R Q12
12 The diagram shows two vertical phone masts, \(AB\) and \(CD\), on horizontal ground.
Diagram NOT accurately drawn
\(AB = 6.2\) m \(AC = 244\) m \(CD = 30.7\) m
Work out the size of the angle of depression of \(B\) from \(D\)
Give your answer correct to one decimal place.
(3)
| Scheme | Marks |
|---|---|
\(\tan \text{‘}{x}\text{’} = \dfrac{30.7 - 6.2}{244}\) or \(\tan \text{‘}{x}\text{’} = \dfrac{244}{30.7 - 6.2}\) or \(\sqrt{244^2 + \text{‘}{24.5}\text{’}^2}\left(= \sqrt{60136.25} = 245.2\ldots\right)\) and \(\sin \text{‘}{x}\text{’} = \dfrac{\text{‘}{24.5}\text{’}}{\text{‘}{\sqrt{60136.25}}\text{’}}\) or \(\cos \text{‘}{x}\text{’} = \dfrac{244}{\text{‘}{\sqrt{60136.25}}\text{’}}\) | M1 |
\(\tan^{-1}\left(\dfrac{\text{‘}{24.5}\text{’}}{244}\right)\) or \(90 - \tan^{-1}\left(\dfrac{244}{\text{‘}{24.5}\text{’}}\right)\) or \(\sqrt{244^2 + \text{‘}{24.5}\text{’}^2}\left(= \sqrt{60136.25} = 245.2\ldots\right)\) and \(\sin^{-1}\left(\dfrac{\text{‘}{24.5}\text{’}}{\text{‘}{\sqrt{60136.25}}\text{’}}\right)\) or \(\cos^{-1}\left(\dfrac{244}{\text{‘}{\sqrt{60136.25}}\text{’}}\right)\) or \(\cos^{-1}\left(\dfrac{\text{‘}{245.2\ldots}\text{’}^2 + \text{‘}{24.5}\text{’}^2 - 244^2}{2 \times \text{‘}{245.2\ldots}\text{’} \times \text{‘}{24.5}\text{’}}\right)\) | M1 |
| 5.7 | A1 |
| (3) | |
| (3 marks) |
Notes
M1: for suitable trig expression for their choice of variable \(x\) to represent either of the (non right-angle) angles in the triangle.
M1: using a suitable trig expression to find the angle of depression.
or for using Pythagoras to find hypotenuse and a suitable trig expression to find the angle of depression.
A1: answers in the range 5.65 to 5.75
SC B2 for 84.3 (or in the range 84.25 to 84.35) or 264.3 (or in the range 264.25 to 264.35) given as answer.