A ladder 11m long leans against a vertical wall at an angle of 75\(^o\) to the ground. The ladder is the pushed 0.2 m up the wall. (a) Illustrate the inform...
Question 1 Report
A ladder 11m long leans against a vertical wall at an angle of 75\(^o\) to the ground. The ladder is the pushed 0.2 m up the wall.
(a) Illustrate the information in a diagram.
(b) Find correct to the nearest whole number, the:
(i) new angle which the ladder makes with the ground:
(ii) distance the foot of the ladder has moved from its original position.
Answer Details
(a) A right-angled triangle: the wall is vertical, the ground horizontal, and the \(11\text{ m}\) ladder is the hypotenuse making \(75^{\circ}\) with the ground. The top rests on the wall; pushing it up raises the top by \(0.2\text{ m}\) and moves the foot nearer the wall.
Original position. Height on wall \(=11\sin 75^{\circ}=11(0.9659)=10.625\text{ m}\).
Foot from wall \(=11\cos 75^{\circ}=11(0.2588)=2.847\text{ m}\).
(b)(i) New angle. New height \(=10.625+0.2=10.825\text{ m}\). The ladder length is unchanged:
\(\sin\theta=\dfrac{10.825}{11}=0.9841 \Rightarrow \theta=79.8^{\circ}\approx \mathbf{80^{\circ}}\).
(b)(ii) Distance the foot moved. New foot from wall \(=11\cos 79.8^{\circ}=11(0.1776)=1.953\text{ m}\).
Distance moved \(=2.847-1.953=0.894\text{ m}\approx \mathbf{1\ m}\).
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