a 20 foot ladder leaning against a building makes and angle of 60 degrees with the ground. How far from the base of the building is the foot of the ladder?
what is 20/cos60 ?
oops 20 cos60
. A 20 ft ladder leaning against a building makes an angle of 60
° with the ground. How far from the base of the building is the foot of the ladder?
To determine how far from the base of the building the foot of the ladder is, we can use trigonometry. In this case, we will use the sine function.
The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. In this scenario, the opposite side is the distance between the base of the building and the foot of the ladder, and the hypotenuse is the length of the ladder, which is 20 feet.
So, we have the following equation:
sin(60 degrees) = opposite / hypotenuse
sin(60 degrees) = opposite / 20 feet
To solve for the opposite side (the distance from the base of the building), we can rearrange the equation:
opposite = sin(60 degrees) * 20 feet
Calculating this, we get:
opposite = 0.866 * 20 feet
opposite ≈ 17.32 feet
Therefore, the foot of the ladder is approximately 17.32 feet from the base of the building.