• Quick retrieval from earlier learning (Trigonometric ratios: SOH CAH TOA). Students answer on mini whiteboards.
• Show answers together and note who needs support in the main task.

1. A ramp rises at 56° over a horizontal distance of 4 m. How high does it rise? Give 1 decimal place. → 5.9Prompt: You know the adjacent side and want the opposite: use tan.
2. A ramp rises at 32° over a horizontal distance of 10 m. How high does it rise? Give 1 decimal place. → 6.2Prompt: You know the adjacent side and want the opposite: use tan.
3. A ramp rises at 35° over a horizontal distance of 7 m. How high does it rise? Give 1 decimal place. → 4.9Prompt: You know the adjacent side and want the opposite: use tan.

• Show a ramp or a ladder against a wall and ask how steep it is.
• Share the objective: Angles of elevation and depression. Read the success criteria together.

• Work through the example out loud, saying why you do each step, not just what you do.
• Example: Maya stands 19 m from the base of a tower. The angle of elevation to the top is 17°. How tall is the tower, to the nearest metre? (Ignore Maya's height.)
• Step 1: h = 19 × tan 17° ≈ 5.81
• Step 2: ≈ 6 m
• Answer: 6
• Pause after each step and ask a student to say what comes next.

• Do these together. Students try each step on whiteboards before you reveal it.
• Use the hints as prompts rather than giving the answer.

1. Yuki stands 43 m from the base of a tower. The angle of elevation to the top is 61°. How tall is the tower, to the nearest metre? (Ignore Yuki's height.) → 78Prompt: Draw the right triangle: ground, tower, line of sight.
2. From the top of a 105 m cliff, the angle of depression to a boat is 17°. How far is the boat from the foot of the cliff? Round to the nearest metre. → 343Prompt: The angle of depression equals the angle of elevation from the boat (alternate angles).

• Students work on the student sheet. Circulate and check the first two answers of every student early.
• Students who finish: write a question of their own for a partner, with the answer.

The 8 questions are on the student sheet below, with answers in the key.

• Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.

1. Elena stands 62 m from the base of a tower. The angle of elevation to the top is 42°. How tall is the tower, to the nearest metre? (Ignore Elena's height.) → 56Prompt: Draw the right triangle: ground, tower, line of sight.
2. From the top of a 24 m cliff, the angle of depression to a boat is 44°. How far is the boat from the foot of the cliff? Round to the nearest metre. → 25Prompt: The angle of depression equals the angle of elevation from the boat (alternate angles).

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-10.