Right-Angled Triangles (Copy)
Q1 (Non-Calculator)
In a right-angled triangle, find the value of sin θ if the opposite side is 5 cm and the hypotenuse is 13 cm.
Solution:
sin θ = opposite ÷ hypotenuse
sin θ = 5 ÷ 13
sin θ ≈ 0.3846
Answer:
sin θ ≈ 0.3846
Q2 (Non-Calculator)
In a right-angled triangle, the adjacent side is 8 cm and the hypotenuse is 10 cm. Find cos θ.
Solution:
cos θ = adjacent ÷ hypotenuse
cos θ = 8 ÷ 10
cos θ = 0.8
Answer:
cos θ = 0.8
Q3 (Non-Calculator)
In a right-angled triangle, the opposite side is 7 cm and the adjacent side is 24 cm. Find tan θ.
Solution:
tan θ = opposite ÷ adjacent
tan θ = 7 ÷ 24
tan θ ≈ 0.2917
Answer:
tan θ ≈ 0.2917
Q4 (Non-Calculator)
Find the length of the side opposite to a 30° angle if the hypotenuse is 10 cm.
Solution:
sin θ = opposite ÷ hypotenuse
sin 30° = opposite ÷ 10
0.5 = opposite ÷ 10
opposite = 0.5 × 10
opposite = 5 cm
Answer:
5 cm
Q5 (Non-Calculator)
In a right-angled triangle, the adjacent side is 5 cm and θ = 60°. Find the hypotenuse.
Solution:
cos θ = adjacent ÷ hypotenuse
cos 60° = 5 ÷ hypotenuse
0.5 = 5 ÷ hypotenuse
hypotenuse = 5 ÷ 0.5
hypotenuse = 10 cm
Answer:
10 cm
Q6 (Calculator)
In a right-angled triangle, the opposite side is 4 cm and the adjacent side is 3 cm. Find the angle θ.
Solution:
tan θ = opposite ÷ adjacent
tan θ = 4 ÷ 3
tan θ ≈ 1.3333
θ = tan⁻¹(1.3333)
θ ≈ 53.1°
Answer:
53.1°
Q7 (Calculator)
In a right-angled triangle, the adjacent side is 7 cm and the hypotenuse is 25 cm. Find the angle θ.
Solution:
cos θ = adjacent ÷ hypotenuse
cos θ = 7 ÷ 25
cos θ = 0.28
θ = cos⁻¹(0.28)
θ ≈ 73.7°
Answer:
73.7°
Q8 (Calculator)
In a right-angled triangle, the opposite side is 12 cm and the hypotenuse is 13 cm. Find the angle θ.
Solution:
sin θ = opposite ÷ hypotenuse
sin θ = 12 ÷ 13
sin θ ≈ 0.9231
θ = sin⁻¹(0.9231)
θ ≈ 67.4°
Answer:
67.4°
Q9 (Calculator)
A ladder leans against a wall. It reaches 3.5 m up the wall and the base is 1.2 m from the wall. Find the angle the ladder makes with the ground.
Solution:
tan θ = opposite ÷ adjacent
tan θ = 3.5 ÷ 1.2
tan θ ≈ 2.9167
θ = tan⁻¹(2.9167)
θ ≈ 71.2°
Answer:
71.2°
Q10 (Calculator)
From a point A, a ship is observed at a bearing of 045° and an angle of elevation of 10° to the top of its mast. If the ship is 500 m away horizontally, find the height of the mast.
Solution:
sin θ = opposite ÷ hypotenuse
sin 10° = height ÷ 500
height = 500 × sin 10°
height ≈ 500 × 0.1736
height ≈ 86.8 m
Answer:
86.8 meters