Trigonometric ratios and right-triangle sides

Label the opposite, adjacent and hypotenuse sides for a chosen acute angle in a right-angled triangle.

Write the three basic ratios: sin θ, cos θ and tan θ.

Explain why the hypotenuse is always opposite the right angle.

Choose the correct ratio for a triangle where the opposite side and hypotenuse are known.

Choose the correct ratio for a triangle where the adjacent side and hypotenuse are known.

Choose the correct ratio for a triangle where the opposite and adjacent sides are known.

Use a calculator to find sin 35° to 3 decimal places.

Rearrange sin θ = opposite ÷ hypotenuse to find the opposite side.

Explain one common mistake students make when choosing opposite and adjacent sides.

State why trigonometric ratios stay constant for similar right triangles.

Find the missing side in a right triangle with hypotenuse 12 cm and angle 38°, where the missing side is opposite the angle.

Find the adjacent side in a right triangle with hypotenuse 15 m and angle 54°. Show the chosen ratio and substitution.

A ladder makes a 70° angle with the ground and reaches 5.8 m up a wall. Find the ladder length to 1 decimal place.

A ramp rises 0.9 m over a horizontal distance of 4.5 m. Find the angle the ramp makes with the ground.

Compare when sine, cosine and tangent are useful by describing the side information needed for each ratio.

Draw a labelled triangle for a trig problem, then solve it and explain why your ratio choice is correct.

A student uses tan when the hypotenuse is involved. Explain why this is wrong and solve a corrected example.

Use Pythagoras and trigonometry in the same triangle to find two missing measurements.

Create a real-world right-triangle problem involving height or distance and solve it using trigonometry.

Write a full worked solution for a right-triangle problem, including diagram labels, ratio, rearrangement, calculation and units.