Question

10. A 50-ft ladder leans against a building so that the base of the ladder is 15 feet from the
building. What angle does the ladder make with the building?

Answer 1

By applying the trigonometry ratio, SOH, the angle that the ladder makes with the building is calculated as: 17.5°

Recall:

• Trigonometry ratios that can be used to solve a right triangle are: SOH CAH TOA.

• SOH represents: sin ∅ = Opp/Hyp

• CAH represents: cos ∅ = Adj/Hyp

• TOA represents: tan ∅ = Opp/Adj

The diagram attached below depicts the problem given.

∅ = x

Opp = 15 ft

Hyp = 50 ft

• Thus, applying the trigonometry ratio, SOH, we have:

sin x = 15/50

x = $sin^{-1}(15/50)$

x = 17.5°

In conclusion, by applying the trigonometry ratio, SOH, the angle that the ladder makes with the building is calculated as: 17.5°

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