Right Triangle Trigonometry

Name:

Date:

WALT & Success Criteria

WALT: We Are Learning To identify and use sine, cosine, and tangent ratios in right-angled triangles to calculate unknown sides and angles.

Success criteria: I can (1) choose the correct trig ratio for a given angle, (2) calculate an unknown side using sin/cos/tan, and (3) find an angle using an inverse trig function and a calculator.

Differentiation: Use triangle manipulatives and calculators; pair students for peer support; provide step-by-step sentence starters for those who need them.

Extension: Use inverse trig to solve for angles in more complex diagrams or start a simple 3D ramp-height problem.

Dyslexia-friendly reading options: Use a ruler or finger to follow lines, read one sentence at a time, and highlight key numbers and words (sin, cos, tan).

📚 Part 1: Quick checks

1. For a right triangle with sides opposite = 4, adjacent = 3, hypotenuse = 5 for angle θ, which is sin θ?

3/5

4/5

3/4

2. Which trig ratio gives adjacent ÷ hypotenuse?

sin

cos

tan

3. Check all statements that are true:

tan θ = opposite / adjacent

sin θ = adjacent / hypotenuse

cos θ = adjacent / hypotenuse

✏️ Part 2: Problem solving

4. Find the length of the side opposite when θ = 30° and hypotenuse = 10 m. (Give your answer to 1 decimal place)

5. A ladder leans against a whare at an angle of 65° to the ground. The ladder is 5.2 m long. How high up the wall does the ladder reach? (m, 1 dp)

6. Find the angle θ in degrees if opposite = 7 cm and adjacent = 24 cm. (Use inverse trig, 1 dp)

7. A carved pou has a support beam that makes a 22° angle with the ground. If the beam reaches 1.5 m high on the pou, how long is the beam? (Give answer in metres, 2 dp)

8. Context problem (Ngāti Manawa): A small waka model uses a right triangular prow. The angle at the base is 40° and the adjacent side along the base is 0.6 m. Find the height of the prow (opposite side). Show working and explain which trig ratio you used.

9. Reflection: Which step did you find hardest today? Write one sentence about how a partner or a manipulative helped you.