Stage 9 - Q1 - 2 marks
Find the missing leg \(x\). All lengths are in cm.
Hint
The hypotenuse is the longest side and lies opposite the right angle.
Stage 9 - Q2 - 2 marks
Find the missing leg \(x\). All lengths are in cm.
Hint
The hypotenuse is the longest side and lies opposite the right angle.
Stage 9 - Q3 - 3 marks
Find \(x\) to 2 d.p. All lengths are in metres.
Hint
Check that the computed leg is shorter than the hypotenuse.
Stage 9 - Q4 - 3 marks
A learner adds 50² and 14² to find \(x\). Explain why subtraction is needed and give the result. Lengths are in cm.
Hint
Write the complete Pythagorean equation before rearranging.
Stage 9 - Q5 - 4 marks
A straight support 23.2 m long reaches from level ground to a vertical wall. Its foot is 16 m from the wall. Find its height above the ground.
Hint
Identify the sloping support as the hypotenuse.
Stage 9 - Q6 - 4 marks
A straight support 5.8 m long reaches from level ground to a vertical wall. Its foot is 4 m from the wall. Find its height above the ground.
Hint
Identify the sloping support as the hypotenuse.
Stage 9 - Q7 - 5 marks
A rectangle has diagonal 123 cm and width 27 cm. Find its other dimension exactly.
Hint
The diagonal is not one of the perpendicular legs.
Stage 9 - Q8 - 5 marks
An isosceles triangle has equal sides 24 cm and base 10 cm. Its altitude bisects the base. Find the exact height.
Hint
The right triangle uses half the given base, not the entire base.
Stage 9 - Q9 - 5 marks
Two sides of a right triangle are 4 cm and 13 cm; their roles are not stated. Find both possible exact third-side lengths.
Hint
Consider which given side could be opposite the right angle.
Stage 9 - Q10 - 3 marks
A 13 m straight support leans against a vertical wall on level ground. Its foot moves from 5 m to 6 m from the wall. Find the exact drop in its top height, then give the drop to the nearest centimetre. Does a 1 m foot movement cause a 1 m height drop?
Hint
Keep the exact second height until subtracting.