- The diagram shows two buildings, each 200 meters tall, with a horizontal distance L between them.
- From the top of the first building, the angle of depression to the base of the second building is 20°, and the angle of elevation to the top of the second building is 10°.
- This creates two right triangles sharing the same horizontal leg L.
- For the lower triangle (to the base): tan(20°) = 200 / L, so L = 200 / tan(20°).
- For the upper triangle (to the top): tan(10°) = (H2 - 200) / L, so H2 - 200 = L * tan(10°).
- Substitute L from the first equation: H2 - 200 = (200 / tan(20°)) * tan(10°).
- Therefore, H2 = 200 + 200 * (tan(10°) / tan(20°)).
- Calculate the values: tan(10°) ≈ 0.1763, tan(20°) ≈ 0.3640.
- H2 = 200 + 200 * (0.1763 / 0.3640) ≈ 200 + 200 * 0.4843 ≈ 200 + 96.86 ≈ 296.86 meters.
- The height of the second building (H2) is approximately 296.86 meters.
Parent Tip: Review the logic above to help your child master the concept of trigonometry worksheet grade 10.
