The angle of elevation of a 15-ft ladder is 70°. Find out
how far the base of the ladder is from the wall.
cos 70° = x/15
To find out how far the base of the ladder is from the wall, we can use trigonometry. We can use the tangent function since we have the angle of elevation and the length of the ladder.
The tangent function is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
In this case, the opposite side is the height of the ladder (15 ft) and the adjacent side is the distance from the base of the ladder to the wall. Let's denote this distance as x.
So, we can set up the equation:
tan(70°) = opposite/adjacent
tan(70°) = 15/x
To solve for x, we can rearrange the equation:
x = 15/tan(70°)
Using a calculator, we can calculate the value of tan(70°):
tan(70°) ≈ 2.747
Now, let's substitute this value back into our equation:
x ≈ 15/2.747
x ≈ 5.459 ft
Therefore, the base of the ladder is approximately 5.459 ft from the wall.
To find out how far the base of the ladder is from the wall, we can use trigonometry.
Let's call the distance from the base of the ladder to the wall "x".
In this problem, we have an angle of elevation (70°) and the length of the ladder (15 ft).
The ladder forms a right triangle with the wall, where the ladder is the hypotenuse, the distance from the base of the ladder to the wall (x) is the adjacent side, and the height of the ladder is the opposite side.
We can use the trigonometric function "tangent" to relate the angle of elevation to the sides of the triangle.
The tangent of an angle is the ratio of the opposite side to the adjacent side.
In this case, tan(70°) = opposite side (15 ft) / adjacent side (x).
Solving for x, we have:
x = (15 ft) / tan(70°).
Using a calculator, we can find the tangent of 70°, which is approximately 2.74747741945.
Now we can substitute this value into the equation:
x = (15 ft) / 2.74747741945.
Evaluating this expression, we find that x is approximately 5.47 ft.
Therefore, the base of the ladder is approximately 5.47 ft from the wall.