1. If AB = 48, find the length of BF
2. Given Circle S with TV = 8, find the area of the circle. Angle V is a 90 degree angle since it is inscribed on a semi­circle. This means you have a 45­45­90 triangle where the hypotenuse is times the side length or . Since this is the diameter of the circle, the radius
would be . The area of a circle is 3. Given WXZY is a trapezoid with WX = WY = 10, find the length of
XZ .
Drop a perpendicular from W to XZ. this will divide the trapezoid into a
45­45­90 triangle and a rectangle. The side of the 45­45­90 triangle is found by dividing the hypotenuse by . which ends up being . Since the opposite sides of rectangles are congruent the length of XZ is the sum of 10 +
4. Given RHOM is a rhombus, with HM = , find the perimeter of the rhombus
If you draw in the other diagonal, then the rhombus is split into 4 : 30 ­
60­90 triangles. Since the diagonals of a rhombus are perpendicular, corner angles are bisected and diagonals are bisected. Half of HM is 5. Given the regular octagon as shown, find the length of ET, if ER = . Divide up the octagon as shown to the right. Using the formula (n­2)180/n you can find one angle of the octagon which is 135 degrees When the vertical line is drawn in part of the angle is 90 and the other 45 so a 45­45­90 triangle gets formed with a side length of 6. The triangle at the bottom left is congruent to the top. The length of ET =
6. Given a square pyramid with the perimeter of the base of 72 and height of 12, find the length of the slant height. Since the perimeter of the base is 72 and the base is a square, each side
is 72/4 or 18 units long. The blue dashed line goes from the center of the square to the side so it is 9 units and the height is given as 12 units. Use the pythagorean theorem on the inner triangle to find the hypotenuse which is also the slant height of the figure. is 72/4 or 18 units long. The blue dashed line goes from the center of the square to the side so it is 9 units and the height is given as 12 units. Use the pythagorean theorem on the inner triangle to find the hypotenuse which is also the slant height of the figure. 7. Find the length of .
To find the diagonal across a rectangular prism take the 8. An equilateral triangle has a perimeter of 6. Find the length of the altitude.
When you draw in the altitude, it splits the triangle into 2 congruent segments. Since the perimeter was 6, each side is 2. The triangle is split into 2 30­60­90 triangles since each angle of an equilateral triangle is 60 degrees. Either use the 30­60­90 triangle ratio or the pythagorean
theorem to find the height. 9. How many vertices does a pentagonal pyramid have?
Each point that you see is a vertex. The number of vertices on a pyramid is always the number of sides on the base + 1
10. Given the cube as shown, if GF is 6 and M is the midpoint of , what is the length of ? Draw in GC. In triangle GCM, The right angle is at M. GC is the diagonal across the front square and it has a length of . AC is the diagonal across the square on the top of the cube and its length is also . MC is since it is half the segment due to M being a midpoint. Using the pythag. theorem 11. Find the measure of . Use the , Since the CosA = .6667, either use the trig tables and work them backwards or use your calculator. Whenever you are looking for an angle you must enter answer of 48 degrees.
. This gives you an 12. Given regular pentagon with center O, find the length of to the
nearest tenth, if the perimeter of the pentagon is 20.
Each angle of a regular pentagon can be found by (n­2)180/n and each angle is 108 degrees. The line drawn from the center out to the angle bisects it so a triangle gets formed with a 54 degree angle. The perpendicular to the side is the apothem and it splits the side of the reg. pentagon in half. Since the perimeter was 20 each side was 4 and the half side is 2. Using the tangent ratio since OX is the opposite side to 54 and TX is the adjacent side you can solve for OX.
x = 2.8
13. If RHOM is a rhombus with a perimeter of 24, find the length of to the nearest tenth. Draw in the other diagonal. This will bisect the corner angle and form right angles at the intersection of the two diagonals. Use the sine ratio to
Draw in the other diagonal. This will bisect the corner angle and form right angles at the intersection of the two diagonals. Use the sine ratio to
find the length of x and then double this to find HM. If the perimeter of the rhombus is 24 then each side is 6.
14. Given the isosceles triangle as shown, find the measure of to the nearest degree. Since trig ratios must be used in right triangles, drop a perpendicular in your isos. triangle. This will split your base in half. The use 15. If the sin A= 0.6, and the AC = 20, find the lengths of If the Sin A = .6 then . Once you have A, use 16. A captain of a ship spots the top of a lighthouse at a 40° angle of elevation. He knows the house if 250 feet above the shore line. How far is the ship from the shore? (nearest foot) Use the Tan ratio since 250 is the opposite side and the shore distance is the adjacent. 17. Find the measure of ÐA to the nearest degree and the length of to the nearest tenth Use the Law of Sines to find A
, The last angle of the triangle will be 97degrees. Repeat the law of Sines
, 18. Find the length of BC. First use the 30­60­90 triangle to find DB which will be 50. The use the right triangle with the 58 degree angle. To find BC you must use the
tangent ratio.