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