1. Knight’s Charge /10/15
A damsel is in distress and is being held captive in a tower. Her knight in shining armor is on the ground below with a ladder. When the knight stands 15 feet from the base of the tower and looks up at his precious damsel, the angle of elevation to her window is 60 degrees. How long does the ladder have to be?
From the foot of a building 50 feet from the base of a tree I have to look upwards at an angle of 22° to sight the top of a tree. From the top of a building, 150 meters above ground level, I have to look down at an angle of depression of 50° to look at the top of the tree.
a. How tall is the building?
b. How tall is the tree?

2. Solving Quadratic Equations by Factoring

3. For any real numbers a and b, if ab=0, then either a=0, b=0, or both.
Zero Product Property
For any real numbers a and b, if ab=0, then either a=0, b=0, or both.

4. The solutions are -3 and 1/2.
In this first example, the equation is already factored and is set equal to zero. To solve, simply set the individual factors equal to zero.
The solutions are -3 and 1/2.

5. Factor using “difference of two squares.”
In this example, you must first factor the equation. Notice the familiar pattern. After factoring, set the individual factors equal to zero.
Factor using “difference of two squares.”

6. In the next example, you must set the equation equal to zero before factoring. Then set the individual factors equal to zero and solve.

7. Re-write this example in the proper form
Re-write this example in the proper form. Notice that the leading coefficient is not one. Use an appropriate factoring technique. Then solve as you have done before.

8. This one uses a different technique than the previous ones
This one uses a different technique than the previous ones. Really, this is something you should consider at the beginning of every factoring problem. See if you can solve it.
Did you take out GCF?

9. Now, try several problems
Now, try several problems. Write these on your own paper, showing all steps carefully.
After completion,
click here.

10. Here are the answers. For help, click on the numbers.1. 2. 3. 4.
5. If all are correct, you’re finished!

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