Year 10 Maths • AC9M10M03 • Authored homework
Practical Pythagoras and right-triangle trigonometry
Solve practical problems using Pythagoras’ theorem and right-angled triangle trigonometry, including angles of elevation/depression, bearings-style diagrams and measurement contexts. Show working, use correct units and check reasonableness.
Part A
Short-answer questions
Write Pythagoras’ theorem for a right-angled triangle.
Find the hypotenuse when the shorter sides are 6 m and 8 m.
State the sine ratio in words.
State the cosine ratio in words.
State the tangent ratio in words.
Identify the opposite side to a given angle in a right triangle.
Choose the correct trig ratio when the opposite and adjacent sides are involved.
Explain what an angle of elevation is.
Explain why the hypotenuse must be the longest side.
Give one real situation that uses right-triangle trigonometry.
Part B
Long-answer questions
A ladder 5 m long leans against a wall with its foot 1.2 m from the wall. Find how high it reaches.
A ramp rises 0.8 m over a horizontal distance of 6 m. Find the angle the ramp makes with the ground.
A tree casts a 14 m shadow when the angle of elevation of the Sun is 35°. Estimate the height of the tree.
A student uses sine when adjacent and hypotenuse are known. Explain how to choose the correct ratio.
A drone is 120 m horizontally from a marker and the angle of elevation is 28°. Estimate its height.
Solve a two-step problem where Pythagoras is needed before applying a trigonometric ratio.
Draw and label a right-triangle model for a practical height or distance problem, then solve it.
Explain how rounding too early can affect a trigonometry answer.
Create a practical problem involving an inaccessible height and solve it with tangent.
Write a full worked solution for a practical right-triangle problem, including diagram description, ratio choice, equation, calculation, units and reasonableness check.
Part C
Research and understanding task
Find a real height or distance that could be estimated using right-triangle trigonometry, such as a tree, building, ramp, drone or flagpole. Draw the triangle model, state assumptions and calculate the unknown measurement.