Theory question 110
Trigonometry(a) In ΔPQS, PQ = 12 cm, PS = 5 cm, ∠SPQ = ∠PRQ = 90°. Find, correct to three significant figures, PR.
(b) The lengths of two ladders, L and M are 10 m and 12 m respectively. They are placed against a wall such that each ladder makes the same angle with the horizontal ground. If the foot of L is 8 m from the foot of the wall, (i) draw a diagram to illustrate this information; (ii) calculate the height at which M touches the wall.
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(a) SQ = √(5² + 12²) = 13 cm
Area: ½ × 5 × 12 = ½ × 13 × PR → PR = 60/13 ≈ 4.62 cm
(b)(i) Two right-angled triangles on the same wall and ground, ladders 10 m and 12 m at equal angles θ to the ground.
(ii) cos θ = 8/10, so sin θ = 0.6
Height of M = 12 × 0.6 = 7.2 m
PR is the height of the right-angled triangle PQS onto its hypotenuse.