Question

A 14 ft ladder leans against a house making an angle of 60° with the ground. How far is the foot of the ladder from the house?

A) 7 ft
B) 10 ft
C) 14 ft
D) 17.32 ft

Answer 1

Using the cosine function for a right triangle, the distance from the foot of a 14 ft ladder to the house, given it makes a 60° angle with the ground, is found to be 7 ft. Therefore, the correct answer is A) 7 ft.

Step-by-step explanation:

Finding the Distance from the Ladder to the House

The question is regarding a 14 ft ladder leaning against a house at a 60° angle with the ground. To find the distance from the foot of the ladder to the house, we can use trigonometry, specifically the cosine function for a right triangle. The ladder serves as the hypotenuse of the triangle, while the distance from the ladder's foot to the house is the adjacent side.

Using the cosine function, we have:

cos(60°) = (Adjacent side) / (Hypotenuse)

cos(60°) = (Distance from the house) / 14 ft

Since cos(60°) is equal to 0.5, the equation becomes:

0.5 = (Distance from the house) / 14 ft

Multiplying both sides by 14 ft gives:

7 ft = Distance from the house

Therefore, the correct answer is A) 7 ft, which means that the foot of the ladder is 7 feet from the house.