You lean a 30 foot ladder against your house and it reaches exactly to the top. The ladder makes a 24˚ angle with the ground. How tall is your house?
(I drew a picture of a house and the ladder)
sin 24 = h/30
h = 30 sin 24 = 12.2 ft
note - do not climb ladder that barely reaches the eaves.
To find the height of your house, we can use trigonometry. The ladder forms a right triangle with the ground and the height of your house.
First, let's label the sides of the right triangle. The hypotenuse is the ladder, which is 30 feet long. The height of the house is the side opposite the angle of 24˚.
Using the trigonometric function, we can use the sine ratio to find the height of the house.
sin(angle) = opposite/hypotenuse
In this case,
sin(24˚) = height of the house/30 feet
To find the height of the house, we rearrange the equation:
height of the house = sin(24˚) * 30 feet
We can use a calculator to find the sine of 24˚:
sin(24˚) ≈ 0.407
Now, we substitute this value into the equation:
height of the house ≈ 0.407 * 30 feet
Calculating this, we find:
height of the house ≈ 12.21 feet
Therefore, the height of your house is approximately 12.21 feet.