(a) In < PQS, |PQ| = 12 cm, |PS| = 5 cm, < SPQ = < PRQ = 90°, Find, correct to three significant figures, |PR|. (b) The length of two ladders, L and M are 10m and 12m respectively. They are placed against a wall such that each ladder makes angle with the horizontal ground. If the foot of L is 8m from the foot of the wall. (i) Draw a diagram to illustrate this information; (ii) Calculate the height at which M touches the wall.
Explanation
(a) In triangle SPQ, (Pythagoras theorem) = Angle b is common to triangles SPQ and PRS are similar. Using (to 3 s.f) (b)(i) (ii) In the smaller triangle, Since these are corresponding angles, x = x in the bigger triangle. = = 7.20 m The ladder M touches the wall at a height 7.2 m above the horizontal ground.
