Question

A ladder is leaning against a wall so that it forms an angle of elevation of 64° with the floor. How far

away is the base of the ladder from the wall if the ladder reaches 8.5 feet high on the wall? Round to
the nearest tenth.

Answer 1

We can use trigonometry to solve this problem. Let x be the distance from the wall to the base of the ladder. Then we have:

tan(64°) = opposite / adjacent

tan(64°) = 8.5 / x

Multiplying both sides by x, we get:

x * tan(64°) = 8.5

Dividing both sides by tan(64°), we get:

x = 8.5 / tan(64°)

Using a calculator, we find that x is approximately 5.3 feet.

Therefore, the base of the ladder is approximately 5.3 feet away from the wall. Rounded to the nearest tenth, this is 5.3 feet.

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