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Answer :
Final answer:
Using the sine function with the given angle of elevation of 70 degrees, the top of the ladder is approximately 30.1 feet off the ground, which does not match any of the provided options A to D.
Explanation:
To find how high off the ground the top of the ladder is, we can use trigonometric functions. The angle of elevation of the ladder is 70 degrees, which corresponds to the angle between the ground and the ladder. The ladder itself is the hypotenuse of a right triangle, and we want to find the opposite side, which represents the height of the ladder against the building.
Using the sine function, which is defined as the ratio of the opposite side to the hypotenuse in a right triangle:
sin(θ) = opposite/hypotenuse
sin(70°) = height/32 ft
height = 32 ft ∙ sin(70°)
Now we calculate:
height ≈ 32 ft ∙ 0.93969 (using a calculator)
height ≈ 30.1 ft
The top of the ladder reaches approximately 30.1 ft off the ground, so none of the options A to D is correct.
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Final answer:
The height of the ladder can be found using the sine function. Substituting the given values into the formula, we find that the top of the ladder is approximately 20.3 feet off the ground.
Explanation:
To find the height of the ladder, we can use trigonometry. Since the ladder is leaning against the building, we can use the sine function to relate the angle of elevation and the height of the ladder. The formula to find the height of the ladder is:
Height = Length of ladder * sin(angle of elevation)
Substituting the given values, we have:
Height = 32 ft * sin(70 degrees)
Calculating this, we get:
Height ≈ 20.3 ft
Therefore, the top of the ladder is approximately 20.3 feet off the ground.
