A ladder leans against a house at a 60° angle to the ground. If the ladder extends to a length of 132 inches, what is the height of the house to the nearest hundredth of an inch?
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To find the height of the house, we can use trigonometry. The angle between the ladder and the ground is 60°, and the length of the ladder is 132 inches.
Let's call the height of the house "h".
Using the sine function, we can write:
sin(60°) = opposite/hypotenuse.
In this case, the opposite side is the height of the house (h) and the hypotenuse is the length of the ladder (132 inches).
So, we can write:
sin(60°) = h/132.
To solve for h, we can rearrange the equation:
h = sin(60°) * 132.
Using a calculator, we find:
h ≈ 0.866 * 132 ≈ 114.912.
Therefore, the height of the house is approximately 114.912 inches.
To find the height of the house, we need to use trigonometry.
Let's draw a right triangle to represent the situation. The ladder forms the hypotenuse of the triangle, and the height of the house is one of the legs. The angle between the ground and the ladder is given as 60°.
Now, we can use the trigonometric function sine (sin) to find the height of the house. Sine is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.
In our case, sin(60°) = height of the house / length of the ladder.
To get the value of sin(60°), we can use a calculator or look it up in a trigonometric table. The sine of 60° is 0.866.
Now we have the equation: 0.866 = height of the house / 132 inches.
To solve for the height of the house, we can rearrange the equation:
height of the house = 0.866 * 132 inches.
Calculating this gives us:
height of the house = 114.312 inches.
Rounding this to the nearest hundredth of an inch, the height of the house is approximately 114.31 inches.