A ladder leaning against a house makes an angle of 60 degrees with the ground. The foot of the ladder to the foundation of the house is 7 feet. How tall is the ladder

The ladder is 8.05 feet tall.

Step-by-step explanation:

The ladder leaning on the house makes a triangle rectangle with the floor and the wall of the house it is leaning against. The ladder is the hypotenuse, the floor is the nearest cathetus and the wall is the oposite cathetus. Since we were given the distance from the base of the ladder to the wall, we have the oposite cathetus, we also know the angle at which the ladder is leaning, so we can use the trigonometric relationship for sin, which is:

sin (theta) = (oposite cathetus) / (hypotenuse)

We want to know the length of the ladder, so we isolate the hypotenuse, we have:

hypotenuse = (oposite cathetus) / sin (theta) = 7/sin (60) = 7/0.87 = 8.05 feet

The ladder is 8.05 feet tall.

L = 14 feet

Step-by-step explanation:

A ladder, the wall of the house and the ground. all form a right triangle in which L (the length of the ladder) is the hypotenuse, the angle β between the bottom of the ladder and the house is 60⁰.

We can calculate L making use of our knowledge of trigonometry,

cos β = adjacent leg / hypotenuse

And cos 60⁰ = 1 / 2

Then we have

1 / 2 = 7 / L ⇒ (1/2) * L = 7 ⇒ L = (2*7)

L = 14 feet