# Algebra

posted by .

A 12' ladder leans against a wall at 68 degree angle of elevation. Find the distance from the ladder's base to the wall.

• Algebra -

Hi Ruth,this is easy!

Imagine a right angle triangle. In this case, the length of the hypothenuse is 12'.Given the angle of elevation 68 degrees. Since it is a right angle triangle,one of the remaining two angles is 90 degrees. So the third angle is 180-90-68 = 22 degrees.
Now we know the angles and we know the length of hypothenuse is 12'. We need to find the distance of ladder's base to the wall. Since two angles and a length is known, we have to use sine formula:
a / sin A = b / sin B
Let a = 12' therefore sin A is sin 90 degrees since it is opposite to the hypothenuse. Let b be the distance needed to be found. So sin B is sin 22 degrees since it is opposite to b.
The answer is b = 4.5'

• Algebra -

or, using this equation

x/12 = cos 68° = 0.374
x = 4.46

• Algebra -

The answer is the same anyway :)

## Similar Questions

1. ### Math Algebra

A 10 foot ladder is to be placed against the wall, the base of the ladder must be placed at an angle of 72 degrees with the level ground for secure footing find to the nearest in how far the base of the ladder should be from the wall …
2. ### algebra

A ladder is resting against a wall. The top of the ladder touches the wall at a height of 15 feet and the length of the ladder is one foot more than twice the distance from the wall. Find the distance from the wall to the bottom of …
3. ### Pre-Calculus

A ladder leans leans against a building that has a wall slanting away from the ladder at an angle of 96 degrees with the ground. If the bottom of the ladder is 23 feet from the base of the wall and it reaches a point 52 feet up the …
4. ### trig

a 30 foot ladder leans against a wall at a 71 degree angle of elevztion find the distance of a ladder's base to the wall
5. ### geom/trig

A 40 ft ladder leans against a wall so the base of the ladder is 11 feet away from the base of the wall . What angle does the ladder make with the wall?
6. ### Geometry

The angle of elevation of a ladder leaning against a wall is 45°. If the distance from the base of the ladder to the wall is 15 feet, find the length of the ladder.
7. ### math

A ladder is 13.0m long. It leans against the wall. The base of the ladder is 3.7m from the wall. What is the angle of inclination of the ladder to the nearest tenth of a degree?
8. ### Maths

A ladder of length 6 m leans against a vertical wall so that the base of ladder is 2m from the wall. calculate the angle between the ladder and the wall.
9. ### math

A ladder of length 6m leans against a vertical wall so that the base of the ladder is 2m from the wall. calculate the angle between the ladder and the wall
10. ### Math

A 25ft ladder leans up against the side of a house, with the base of the ladder a distance 3ft from the wall. If the ladder is moved out by 5ft, how far down the wall will the top of the ladder move?

More Similar Questions