A slope is built against a wall which makes a 30° angle with the ground. If the height of the wall is 2 meters, find the length of the slope. (Your answer will be numerical only.) Answer:Question 43
Question
A slope is built against a wall which makes a 30° angle with the ground. If the height of the wall is 2 meters, find the length of the slope. (Your answer will be numerical only.) Answer:Question 43
Solution
The problem involves a right triangle, where the wall is the opposite side, the ground is the adjacent side, and the slope is the hypotenuse.
Given that the angle (θ) is 30° and the height of the wall (opposite side) is 2 meters, we can use the sine function to find the length of the slope (hypotenuse).
The sine function is defined as sin(θ) = opposite/hypotenuse.
Rearranging the formula to solve for the hypotenuse gives us: hypotenuse = opposite/sin(θ).
Substituting the given values into the formula gives us: hypotenuse = 2/sin(30°).
Since sin(30°) = 0.5, the calculation becomes: hypotenuse = 2/0.5 = 4 meters.
So, the length of the slope is 4 meters.
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