Question

A 17-foot ladder is propped up against a wall so that the base of the ladder is 8 ft from the wall. The base of the ladder makes an angle 8 (measured in radians) with the ground. (a) Draw a picture of the situation. Be sure to label the pertinent information. (b) How far above the ground is the top of the ladder? (e) What is the measure of 0?

Answer 1

(a) Here is a diagram of the situation:

```
|\
| \
| \ <-- Ladder (17 ft)
| \
| \
| \
| \
| \
| \
|θ \
|________\
8 ft Wall
```

In the diagram, the ladder is represented by a diagonal line, the wall is the vertical line on the right side, and the ground is the horizontal line at the bottom. The base of the ladder is labeled as 8 ft, and the angle between the ground and the ladder is labeled as θ.

(b) To find how far above the ground the top of the ladder is, we can use trigonometry. The opposite side to the angle θ is the vertical distance from the ground to the top of the ladder.

Using the sine function:
sin(θ) = opposite/hypotenuse
sin(θ) = height of ladder/17 ft

Rearranging the equation:
height of ladder = 17 ft * sin(θ)

(c) The measure of θ, the angle, is already given as 8 radians.