can someone please explain how to do this problem:
A twelve-foot ladder is leaning against a wall. If the ladder reaches 8 ft high on the wall, what is the angle the ladder forms with the ground to the nearest degree?
1. 36°
2. 42°
3. 48°
4. 54°
Draw a rt triangle with the ladder as
the hyp(12ft) and 8ft. as the ver side.
sinA = Y/r = 8/12 = 0.6666,
A = 41.81 deg or 42deg.
To find the angle the ladder forms with the ground, we can use trigonometry. Specifically, we can use the sine function.
Step 1: Draw a right triangle where the ladder is the hypotenuse, the height on the wall is the opposite side, and the distance from the base of the ladder to the wall is the adjacent side.
Step 2: Identify the given values. The height on the wall is 8 ft, and the length of the ladder is 12 ft.
Step 3: Use the sine function to find the angle. The sine function is defined as the ratio of the opposite side to the hypotenuse. In this case, sin(angle) = opposite/hypotenuse. Therefore, sin(angle) = 8/12.
Step 4: Solve for the angle by taking the inverse sine of both sides. angle = sin^(-1)(8/12).
Step 5: Use a calculator to find the inverse sine of 8/12. The result is approximately 48.189685°.
Step 6: Round the result to the nearest degree. The angle is approximately 48°.
Therefore, the correct answer is option 3.