SOLUTION: A ladder 20 feet long leans against the side of a building, and the angle between the ladder and the building is 22 degrees. a) find the distance from the bottom of the ladder to

Question 78178: A ladder 20 feet long leans against the side of a building, and the angle between the ladder and the building is 22 degrees. a) find the distance from the bottom of the ladder to the building to the nearest tenth. b) If the distance from the bottom of the ladder to the building is increased by 3 feet, how far does the top of the ladder move down the building? This is what I have done a) sin90/20= sin22/b
20sin22/sin90 =b
7.49=b
Is this correct?

b)sin22/10.5 = sin90/a
10.5sin90/sin22=a
22.03=a
Is this correct?

Can you help me? This is a worksheet problem assigned by my teacher.

Answer by 303795(562) (Show Source):
You can put this solution on YOUR website!
Part A looks good.(nearest tenth implies 1 decimal place)
The 20 foot ladder has moved 22 ft down the building!!!!
After the bottom of the ladder has moved out an extra 3 feet the angle at the top is no longer 22 degrees.
You have a right angle triangle with a hypotenuse of 20 feet and a base of 10.5 feet. Use Pythagoras to solve this one.

b=17 feet
In the same way find the original height of the ladder on the building.

b=18.5 feet
So the ladder has slipped down an extra 1.5 feet.