Question

A ladder leans against the side of a house. The angle of elevation of the ladder is 73°, and the top of the length is 14 ft Find the distance from the bottom of the ladder to the side of the house. Round your answer to the nearest tenth.

Answer 1

about 4.3 feet

Explanation:

The figure is omitted--please sketch it to confirm my answer.

Set your calculator to degree mode.

`\tan(73) = (14)/(x)`

`x \tan(73) = 14`

`x = (14)/( \tan(73) ) = 4.28`

Answer 2

We can use trigonometry to solve the problem. Let's assume that the distance from the bottom of the ladder to the side of the house is "x" feet. Then, we can use the tangent function to relate the angle of elevation and the distance x:

tan(73°) = (opposite side) / (adjacent side)

where the opposite side is the height of the ladder (which is 14 feet) and the adjacent side is the distance x.

Rearranging the equation, we get:

opposite side = x tan(73°)

Now, we can use the Pythagorean theorem to relate the distance x, the opposite side (which is the length of the ladder), and the hypotenuse:

x^2 + (14 ft)^2 = (length of the ladder)^2

Substituting the expression for the length of the ladder, we get:

x^2 + (14 ft)^2 = (x tan(73°))^2 + (14 ft)^2

Simplifying the equation:

x^2 = (x tan(73°))^2

x = length of the ladder / tan(73°)

x ≈ 3.9 ft (rounded to one decimal place)

Therefore, the distance from the bottom of the ladder to the side of the house is approximately 3.9 feet.