Question

A 14 ft ladder is used to scale a 13 ft wall. At what angle of elevation must the laxder be situated in order to reach the top of the wall?

Answer 1

`\theta \approx 68^\circ`

Explanation:

Trigonometry

The ladder, the wall, and the ground form a right triangle, where the ladder is the longest side (hypotenuse).

The trigonometric ratios stand on right triangles and can be used to relate side lengths with angles.

The angle of elevation, formed by the ladder and the ground has the height of the wall as the opposite side. Thus we can use the sine ratio, defined as:

`\displaystyle \sin\theta=\frac{\text{opposite leg}}{\text{hypotenuse}}`

`\displaystyle \sin\theta=(13)/(14)`

Solving:

`\displaystyle \theta=\arcsin (13)/(14)`

Calculating:

`\mathbf{\theta \approx 68^\circ}`

Answer 2

The angle of elevation is equal to 68.2 degrees

Explanation:

As you can see from the image below we are trying to find the angle on the bottom right.

We know that the hypotenuse is equal to 14 and we know that the opposite is equal to 14. This means that we will be using Sine.

sin x = 13/14

divide:

sin x = 0.9285714286

now we need to use sin^-1

sin^-1 (0.9285714286) = 68.21321071

Round 68.21321071 to the nearest tenth:

68.2

The angle of elevation is 68.2 degrees!