The height the 15 ft building touches the building is approximately 10 ft.
The ladder is 9 ft tall and leaning on a wall that is 6 ft above the ground.
The situation forms a right angle triangle.
Properties of a right angle triangle:
- One of it angle is equals to 90 degrees.
- The sides and angles can be found using trigonometric ratios.
Therefore, let's find the angle made by the 9 ft ladder and then use it to find the height the 15 ft ladder touch the building.
Using trigonometric ratios,
let
∅ = angle
tan ∅ = opposite / adjacent
tan ∅ = 6 / 9 = 2 / 3
∅ = tan⁻¹ 0.6666666
∅ = 33.6900672615
Therefore, the height the 15 ft ladder touch building can be calculated as follows:
tan 33.69 = h / 15
h = 15 × 0.66666496431
h = 9.99997446476
h ≈ 10 ft.
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