A 25 foot ladder is leaning against a house at a 63 degree angle. How far up does it reach off the ground?
sin 63 = h/25
To find out how far up the ladder reaches off the ground, we can use trigonometry, specifically the sine function.
The sine of an angle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, the side opposite the angle is the height of the ladder off the ground, and the hypotenuse is the length of the ladder.
Let's call the height of the ladder off the ground "h" and the length of the ladder "25 feet". The angle between the ladder and the ground is 63 degrees.
So, we can write the equation as:
sin(63°) = h / 25
To solve for h, we need to isolate it. Multiply both sides of the equation by 25:
25 * sin(63°) = h
Using a calculator to evaluate sin(63°), we find that sin(63°) is approximately 0.8910. Substituting this value:
25 * 0.8910 = h
So, the height of the ladder off the ground is approximately:
h = 22.275 feet
Therefore, the ladder reaches approximately 22.275 feet off the ground.
To find out how far up the ladder reaches off the ground, you'll need to use trigonometry. Specifically, you can use the sine function.
The sine function relates the length of the side opposite an angle in a right triangle (in this case, the height of the ladder off the ground) to the length of the hypotenuse (which is the ladder itself). The formula is:
sin(angle) = opposite/hypotenuse
In your case, the angle is 63 degrees and the hypotenuse is the length of the ladder, which is 25 feet. Rearranging the formula to solve for the opposite side, you get:
opposite = sin(angle) * hypotenuse
Now, substitute the values into the formula and calculate the height:
opposite = sin(63 degrees) * 25 feet
Using a calculator, find the sine of 63 degrees and multiply it by 25 feet:
opposite ≈ 0.891 * 25 feet ≈ 22.275 feet
Therefore, the ladder reaches approximately 22.275 feet off the ground.