A 16 - foot ladder leaning against the side of a house reaches 12 feet
up the side of the house. What angle does the ladder make with the
ground
48
To find the angle that the ladder makes with the ground, we can use trigonometry. The ladder, the side of the house, and the ground form a right triangle. The length of the ladder is the hypotenuse, and the height of the ladder up the side of the house is one of the legs.
Using the Pythagorean theorem, we can find the length of the other leg (the distance the ladder extends horizontally on the ground).
Let's call the length of the other leg "x."
Using the Pythagorean theorem:
x^2 + 12^2 = 16^2
Simplifying the equation:
x^2 + 144 = 256
Subtracting 144 from both sides:
x^2 = 112
Taking the square root of both sides:
x = √112
Simplifying the square root of 112:
x ≈ 10.583
Now that we know the length of the side adjacent to the angle, we can use trigonometry to find the angle:
cos(angle) = adjacent/hypotenuse
cos(angle) = x/16
Substituting the value of x:
cos(angle) = 10.583/16
Finding the angle:
angle = arccos(10.583/16)
Calculating the arccos (inverse cosine) of 10.583/16:
angle ≈ 47.86 degrees
Therefore, the angle that the ladder makes with the ground is approximately 47.86 degrees.
To find the angle that the ladder makes with the ground, we can use trigonometric functions. In this case, we can use the sine function.
The sine function relates the angle with the opposite side and the hypotenuse of a right triangle. In this scenario, the ladder is the hypotenuse of the right triangle, and the height of the ladder against the side of the house is the opposite side.
Let's denote the angle as θ.
Using the sine function: sin(θ) = opposite/hypotenuse
We know that the opposite side is 12 feet, and the hypotenuse (the ladder) is 16 feet.
sin(θ) = 12/16
We can simplify this equation:
sin(θ) = 3/4
Now, to find the angle θ, we need to find the inverse sine (or arcsine) of 3/4. This is denoted as sin^(-1)(3/4) or arcsin(3/4) on most calculators.
arcsin(3/4) ≈ 48.59°
So, the angle that the ladder makes with the ground is approximately 48.59°.
Draw a picture of a right triangle.
The hypotenuse (the longest side opposite of the ninety degree angle) would be 16.
The opposite of the desired angle is 12.
The sine of what angle equals 12/16 (6/8 3/4)?