Final answer:
The angle the ladder makes with the ground can be found using trigonometry. By calculating the other leg of the triangle with the Pythagorean theorem and then taking the inverse tangent of the opposite over adjacent sides, the angle is approximately 36 degrees. Therefore correct option is B
Step-by-step explanation:
A 17-foot ladder leans against a building and touches it at a point 10 feet high. To find the approximate angle the ladder makes with the ground, we can use trigonometry, specifically the tangent function, which relates the angle of a right triangle to the ratio of the opposite side (height where the ladder touches the building) to the adjacent side (distance from the base of the building to the bottom of the ladder).
Using the Pythagorean theorem, we first find the distance from the base of the building to the bottom of the ladder. We have a right triangle with a hypotenuse of 17 feet and one of the legs as 10 feet.
Hence, the other leg (distance from the building) is √(17² - 10²) = √(289 - 100)
= √189
≈ 13.75 feet.
Now, we can calculate the angle using the tangent function: tan(θ) = opposite/adjacent
= 10/13.75.
Using a calculator or inverse tangent function, we find that θ ≈ 36°.
Therefore, the appropriate answer among the choices is B. 36°.