Question

A ladder leans against the wall of a building. The ladder measures 47 inches and forms an angle of 51 degrees with the ground. How far from the ground, in inches, is the top of the ladder? How far from the wall, in inches, is the base of the ladder? Round to two decimal places as needed.

Ground to top in inches:
Base to wall in inches:

Answer 1

• to top: 36.53 inches
• to base: 29.58 inches

Explanation:

You want the distances from the ground to the top of the ladder, and from the wall to the base of the ladder when the 47-inch ladder makes an angle of 51° with the ground.

Trig functions

The trig functions Sine and Cosine relate the sides of a right triangle to the angle and the hypotenuse:

Sin = Opposite/Hypotenuse

Cos = Adjacent/Hypotenuse

Multiplying by the hypotenuse gives ...

opposite (ground to top) = (47 in) × sin(51°) = 36.53 in

adjacent (wall to base) = (47 in) × cos(51°) = 29.58 in

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Additional comment

These trig relations are summarized in the mnemonic SOH CAH TOA.