A 7.4 m ladder is placed against a wall so that it forms a 68.7o 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 7.4 m ladder is placed against a wall so that it forms a 68.7o 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 acts as the hypotenuse, the distance from the wall to the base of the ladder is the adjacent side, and the angle is 68.7 degrees.
The formula is:
cos(θ) = adjacent/hypotenuse
We can rearrange the formula to solve for the adjacent side (the distance from the wall to the base of the ladder):
adjacent = hypotenuse * cos(θ)
Substituting the given values:
adjacent = 7.4m * cos(68.7°)
Now, calculate the cosine of 68.7 degrees and multiply it by 7.4.
After calculating, you should get the distance from the wall to the base of the ladder. Remember to round your answer to the nearest tenth.
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