The end panel of a livestock water trough is a right-angled triangle. It is \(1.1\) m tall and \(0.6\) m wide at the base. 0.6 m1.1 mbrace© EAGLE BEACON GLO...
Question 1 Report
The end panel of a livestock water trough is a right-angled triangle. It is \(1.1\) m tall and \(0.6\) m wide at the base.
- Work out the length of a diagonal brace fitted across the end panel. Give your answer correct to \(3\) significant figures. (2)
- Find the angle the brace makes with the base of the panel. Give your answer correct to \(1\) decimal place. (3)
Answer Details
This question tests Pythagoras' theorem for a diagonal brace, then the tangent ratio and its inverse to find the angle that brace makes with the base.
(a) The brace is the hypotenuse of the right-angled triangle with the panel's height (1.1 m) and base width (0.6 m) as its shorter sides:
\[ \text{brace} = \sqrt{0.6^2 + 1.1^2} = \sqrt{1.57} \approx 1.25 \text{ m} \ (3\text{ s.f.}) \] [2 marks]
(b) The angle the brace makes with the base has the height (1.1 m) opposite it and the base width (0.6 m) adjacent to it:
\[ \tan \theta = \frac{1.1}{0.6} \]
\[ \theta = \tan^{-1}\left(\frac{1.1}{0.6}\right) \approx 61.4^\circ \ (1\text{ d.p.}) \] [3 marks]
Since the panel is taller than it is wide, the brace leans towards the vertical, which is consistent with an angle of \( 61.4^\circ \), well above \( 45^\circ \).
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