Suppose a 25-foot ladder is leaning against a wall making a 63 degree angle with the wall. How high up th wall is the end of the ladder?
To find out how high up the wall the end of the ladder reaches, we need to use trigonometry. Specifically, we'll use the sine function because we have the angle and the length of the ladder. Here's how we can solve this step by step:
1. Draw a right triangle. Label one side as the height we want to find (let's call it "h"), the other side as the length of the ladder (25 feet), and the angle between these two sides as 63 degrees.
2. Identify the relevant trigonometric ratio. In this case, since we have the angle and the length of the ladder, we'll use the sine function: sin(angle) = opposite/hypotenuse.
3. Substitute the known values into the trigonometric equation. We have sin(63 degrees) = h/25 feet.
4. Solve for the height by multiplying both sides of the equation by 25 feet: h = 25 feet * sin(63 degrees).
5. Use a calculator to find the sine of 63 degrees, then multiply that value by 25 feet to get the height. The calculated height will be approximately 22.6 feet.
Therefore, the end of the ladder reaches approximately 22.6 feet up the wall.
To find the height at which the ladder reaches on the wall, we can use trigonometry.
Given that the ladder makes a 63-degree angle with the wall, we can identify the adjacent side as the distance along the wall and the hypotenuse as the length of the ladder.
Using the cosine function:
cos(θ) = adjacent/hypotenuse
cos(63°) = adjacent/25ft
Rearranging the equation to solve for the adjacent side:
adjacent = cos(63°) * 25ft
Using a calculator:
adjacent ≈ 12.97ft
Therefore, the end of the ladder is approximately 12.97 feet high on the wall.