BitWithBite
Mathematics Worksheet
🗼 Heights & Distances
SCORE___ / 20
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After this worksheet you can
Use angles of elevation and depression.Use tan to find heights.Solve real-world distance problems.Identify the information needed to solve.📚 Quick Recap
Heights and distances problems use trigonometry to measure things that are hard or impossible to measure directly — like the height of a building or the distance across a river.
🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
160 m from a building, elevation 35°. The height is:
2From a 120 m lighthouse, depression to a ship is 15°. The distance is:
3A ladder at 70°, foot 3 m from the wall, reaches:
4A tower's shadow is 25 m when the sun's elevation is 40°. The height is:
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5The angle measured upward from the horizontal is the angle of .
6The angle measured downward from the horizontal is the angle of .
7A person 60 m from a building measures a 35° angle of elevation. Find the height.
8From a 120 m lighthouse, the depression to a ship is 15°. Find the distance to the ship.
9A ladder makes 70° with the ground, its foot 3 m from the wall. Find how high it reaches.
🚀 Section C · Challenge ● CHALLENGE 5
10A tower casts a 25 m shadow when the sun's elevation is 40°. Find the tower's height.
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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✂ answer key — fold or cut before handing out
1-A 2-A 3-A 4-A | 5 elevation 6 depression 7 = 60·tan(35°) ≈ 42 m 8 = 120/tan(15°) ≈ 447.8 m 9 = 3·tan(70°) ≈ 8.24 m | 10 = 25·tan(40°) ≈ 20.98 m