A laffer leaning against a house maes an angle of 60 degress with the ground. The foot of the leadder is 7 feet from the foundation of the house. How long is the ladder? Please help
To find the length of the ladder, we can use the concept of trigonometry, specifically the sine function.
Let's call the length of the ladder "L". The angle between the ladder and the ground is 60 degrees, and the distance from the foot of the ladder to the house is 7 feet.
Using the sine function, we can set up the equation:
sin(angle) = opposite/hypotenuse
In this case, the opposite side is the height of the house, and the hypotenuse is the length of the ladder.
We can rearrange the equation to solve for the hypotenuse:
hypotenuse = opposite / sin(angle)
Since we have the opposite side as the height of the house, we need to find the height of the house using the angle and the distance from the foot of the ladder to the house.
To find the height, we can use the cosine function:
cos(angle) = adjacent/hypotenuse
In this case, the adjacent side is the distance from the foot of the ladder to the house, and the hypotenuse is the length of the ladder.
We can rearrange the equation to solve for the adjacent side:
adjacent = hypotenuse * cos(angle)
Now we can substitute the known values into the equations to find the length of the ladder.
First, let's find the height of the house:
height = adjacent = 7 feet
Next, we can calculate the hypotenuse (length of the ladder):
hypotenuse = height / sin(angle) = 7 / sin(60 degrees) = 7 / 0.866 = 8.077 feet (rounded to three decimal places)
Therefore, the length of the ladder is approximately 8.077 feet.