A ladder 6m long leans against a vertical wall at an angle 53º to the horizontal. How high up the wall does the ladder reach?

Answer Details

To find how high up the wall the ladder reaches, we can use trigonometry, specifically the sine function. Given: Length of the ladder = 6m Angle between the ladder and the horizontal = 53º We want to find the height of the ladder on the wall. Using the trigonometric relationship for right triangles, we can use the sine function to relate the angle and the sides of the triangle. sin(angle) = opposite / hypotenuse In this case, the height of the ladder on the wall is the opposite side, and the length of the ladder is the hypotenuse. sin(53º) = height / 6 To find the height, we rearrange the equation: height = sin(53º) * 6 Using a calculator, we can evaluate sin(53º) ≈ 0.7986. height ≈ 0.7986 * 6 ≈ 4.7916 Therefore, the height up the wall that the ladder reaches is approximately 4.7916m. So, the correct answer is 4.792m.