Pythagoras' Theorem and Right-Angled Triangle Trigonometry — Solutions

Full worked solutions, with method and final answer for every part.

Question 1

(a)Use Pythagoras: hyp² = 3² + 4².

hyp = √25 = 5 cm

Question 2

(a)sin(angle) = opposite/hypotenuse = 5/8, so angle = sin⁻¹(5/8).

≈ 38.7°

Question 3

(a)tan(angle) = opposite/adjacent = 2.0/3.5, so angle = tan⁻¹(2.0/3.5).

≈ 29.7°

Question 4

(a)Use Pythagoras: hyp² = 5² + 12².

√169 = 13 cm

Question 5

(a)Rearrange Pythagoras: third² = 13² − 5².

√144 = 12 cm

Question 6

(a)cos(angle) = adjacent/hypotenuse = 6/10, so angle = cos⁻¹(0.6).

≈ 53.1°

Question 7

(a)tan(angle) = opposite/adjacent, so opposite = 50 × tan(25°).

≈ 23.3 m

Question 8

(a)opposite = hypotenuse × sin(angle).

10 × sin40° ≈ 6.43 cm (3 s.f.)

Question 9

(a)adjacent = hypotenuse × cos(angle).

10 × cos40° ≈ 7.66 cm (3 s.f.)

Question 10

(a)tan(angle) = height/distance, so angle = tan⁻¹(100/200).

≈ 26.6° (3 s.f.)

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