Surds
Simplify: √16
Answer: 4
In a right-angled triangle, which side is the hypotenuse?
Answer: The longest side — the one opposite the right angle
Which ratio does SOH represent, and what is the formula?
Answer: Sine = Opposite ÷ Hypotenuse
What does the "T" mean in a bearing like 045°T?
Answer: True — the bearing is measured clockwise from North
State Pythagoras' theorem (the formula).
Answer: a² + b² = c²
Simplify: √20
Answer: 2√5
A right triangle has legs of 3 cm and 4 cm. Find the hypotenuse.
Answer: 5 cm
A right triangle has a hypotenuse of 10 cm and an angle of 30°. Find the length of the side opposite the angle.
Answer: 5.00 cm (10 × sin 30°)
How many degrees are there in a full bearing circle?
Answer: 360°
Simplify: √45
Answer: 3√5
Simplify: √72
Answer: 6√2
A right triangle has legs of 6 m and 8 m. Find the hypotenuse.
Answer: 10 m
A right triangle has an angle of 40° and the adjacent side is 8 cm. Find the hypotenuse.
Answer: 10.44 cm (8 ÷ cos 40°)
Convert the compass bearing N30°E into a true bearing.
Answer: 030°T
A right triangle has legs of 5 cm and 12 cm. Find the hypotenuse.
Answer: 13 cm
Simplify: √3 + 5√3
Answer: 6√3
A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. Find the other leg.
Answer: 12 cm
A right triangle has an opposite side of 7 cm and an adjacent side of 10 cm. Find the angle (nearest degree).
Answer: 35° (tan⁻¹(7/10))
A hiker walks on a bearing of 250°T. What bearing (the "back bearing") would take her directly back to her starting point?
Answer: 070°T (250° − 180°)
A right triangle has an angle of 50° and an adjacent side of 15 cm. Find the length of the opposite side, correct to 2 decimal places.
Answer: 17.88 cm (15 × tan 50°)
Evaluate: √2 × √8 ÷ √4
Answer: 2
A triangle has sides 9 cm, 12 cm, and 15 cm. Use Pythagoras' theorem to show whether it is right-angled.
Answer: Yes — 9² + 12² = 81 + 144 = 225 = 15², so it is right-angled
From a point 20 m from the base of a tower, the angle of elevation to the top is 35°. Find the height of the tower, correct to 1 decimal place.
Answer: 14.0 m (20 × tan 35°)
A ship sails 40 km on a bearing of 120°T. How far east of its starting point has it travelled, correct to 2 decimal places?
Answer: 34.64 km (40 × sin 120°)
A boat travels 25 km on a bearing of 200°T. How far south of its starting point has it travelled, correct to 2 decimal places?
Answer: 23.49 km (25 × cos 20°, since 200°T is 20° past due south)