A 7 m ladder is placed against a wall so that it forms a 67o angle with the ground. How far is the base of the ladder from the wall?(Round your answer to the nearest tenth and enter only the number with no units in the blank.)
Question
A 7 m ladder is placed against a wall so that it forms a 67o angle with the ground. How far is the base of the ladder from the wall?(Round your answer to the nearest tenth and enter only the number with no units in the blank.)
Solution
To solve this problem, we can use the trigonometric function cosine. The cosine of an angle in a right triangle is defined as the adjacent side length divided by the hypotenuse length. In this case, the ladder is the hypotenuse, the wall is the adjacent side, and the distance from the wall to the base of the ladder is the opposite side.
The formula for cosine is:
cos(θ) = adjacent/hypotenuse
We know the hypotenuse (7 m) and the angle (67 degrees), and we want to find the adjacent side (the distance from the wall to the base of the ladder).
Rearranging the formula to solve for the adjacent side gives us:
adjacent = hypotenuse * cos(θ)
Substituting the given values into the formula gives us:
adjacent = 7 m * cos(67 degrees)
Using a calculator to find the cosine of 67 degrees and multiplying by 7 gives us the distance from the wall to the base of the ladder.
Remember to round your answer to the nearest tenth.
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