We have a right triangle formed by the ladder against the wall. The base of the triangle is 4 feet, while the angle of elevation from the bottom of the ladder to the roof is 63°. We'll call the side opposite to this angle as the height of the triangle h and the ladder as the hypotenuse L. We want to find L.
To solve this problem, we can use the sine function, which relates the angle, the opposite side, and the hypotenuse in a right triangle:
sin(angle) = opposite/hypotenuse
Let's plug in the values we know:
sin(63°) = h/L
We want to find L, so we need to get it alone on one side of the equation. To do this, we can multiply both sides by L:
L * sin(63°) = h
Now we need to find the height of the triangle h. We can use the tangent function, which relates the angle, the opposite side, and the adjacent side in a right triangle:
tan(angle) = opposite/adjacent
Plugging the values:
tan(63°) = h/4
To solve for h, we multiply both sides by 4:
4 * tan(63°) = h
Now that we have an expression for h, we can plug it back into the sine equation:
L * sin(63°) = 4 * tan(63°)
To solve for L, divide both sides by sin(63°):
L = (4 * tan(63°))/sin(63°)
Using a calculator to find the values:
L ≈ (4 * 1.9626)/0.8912
L ≈ 8.7934
Therefore, the ladder is approximately 8.79 feet long.
2) A roofer props a ladder against a wall so that the base of the ladder is 4 feet away from the building. If the angle of elevation from the bottom of the ladder to the roof is 63°, how long is the ladder?
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