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.
Explanation
(a) The required diagram was
(b)(i) we have sin 75\(^o\) = \(\frac{x}{11}\) and this will give x = 10.625m. Since the ladder has moved up by 0.2 , the new point where the ladder touches the wall is 0.2 + 10.625 = 10.825m.
Then sin\(\theta\) = \(\frac{10.825}{11}\)
Sin\(\theta\) = 0.9841 and \(\theta\) = sin\(^{-1}\)(0.9841) = 79.77\(^o\) = 80\(^o\)
(b)(ii) Cos 75\(^o\) = \(\frac{y}{11}\) so that y = 2.2847m
Similarity, cos 79.77 = \(\frac{q}{11}\) and q = 1.9536m. Therefore, the distance the ladder was dragged = 2.8470 - 1.9536 = 0.8934m = 1m