A 15 ft ladder makes a 52° angle with the ground. How far will the top of the ladder be above the ground.

11.820 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

Sin = Opposite/Hypotenuse

The length of the ladder is the hypotenuse of a right triangle with 52° as the base angle. The side opposite is the height up the building where the top of the ladder rests. So, you have the relation ...

sin (52°) = height / (15 ft)

Multiplying by the denominator gives you ...

height = (15 ft) ·sin (52°) ≈ 11.820 ft

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You may need to round this number appropriately.