Find the geometric mean for each pair of numbers. Leave in simplified radical form.
1. 3 and 12
2. 5 and 4
3. 28 and 56.
4.In the box to the
right, all sides are perpendicular.What is the length of the longest curtain
rod that will fit in the box?
5. In the drawing below use the coordinates and the Pythagorean theorem to derive the formula for the distance from A to B.
6. A 
triangle has a shorter leg that is 8 units long.
Find the lengths of the hypotenuse and the longer leg.
7. In a Chinese legend the famous general Han Xin flew a kite over his enemies palace to calculate how far his troops were from the palace.
a. Suppose the general knew the length of the kite string and the angle the kite string made with the ground. Draw a picture of the situation and label it with what is known and what he is trying to find.
b. Suppose the string made a
angle with the ground and was 1800 ft. long. How far away were General Han Xin's troops from the palace?
Write two equations you could use to thing the length x. Find x.
8. 
9.
10.
Find the trigonometric ratio as a fraction and a decimal rounded to the nearest thousandth
11.
sin A
12.cos A
13. tan B
14. tan A
15. A regular hexagon is composed of six equilateral triangles. Find the perimeter of the hexagon if the altitude of one of the equilateral triangles, the apothem, is 8 cm.
16. Write the sine of A and cosine of A in terms
of ratios with a,b,c.
What is 
equal to? Hint: Use the Pythagorean Theorem.