Question

A ladder leans against the side of a house. The angle of elevation of the ladder is 74° when the bottom of the ladder is 12 ft from the side of the house. Find the length of the ladder. Round your answer to the nearest tenth.

?
12
74°

Answer 1

Answer: We can use trigonometry to solve this problem.

Let x be the length of the ladder, and h be the height of the ladder.

We can use the tangent function to relate the angle of elevation, the length of the ladder, and the height of the ladder:

tan(74°) = h / x

We know that x = 12 ft and we can find h.

We can cross multiply and solve for h:

x * tan(74°) = h

12 * tan(74°) = h

We can use a calculator to find the value of h, this will give us the height of the ladder.

Finally, we can use the Pythagorean theorem to find the length of the ladder:

x^2 = h^2 + 12^2

x = √(h^2 + 12^2)

Round your answer to the nearest tenth, we have x = √(h^2 + 12^2)

We can use the value of h to find the length of the ladder.

However, without the value of h it is not possible to find the length of the ladder.

Explanation: