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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 semi-circle. This means you have a 45-45-90 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 
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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 45-45-90 triangle and a rectangle. The side of
the 45-45-90 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 +
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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 : 30-60-90 triangles. Since the diagonals of a
rhombus are perpendicular, corner angles are bisected and diagonals are
bisected. Half of HM is 
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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
(n-2)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 45-45-90 triangle gets formed with a side length of 6. The
triangle at the bottom left is congruent to the top. The length of ET =
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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.
  |
.
To find the
diagonal across a rectangular prism take the
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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 30-60-90 triangles since each angle of an
equilateral triangle is 60 degrees. Either use the 30-60-90 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
 |
. 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 
. This gives you an answer of
48 degrees.
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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
(n-2)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
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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 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.
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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 
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A= 0.6, and the AC =
20, find the lengths of
If the Sin A = .6 then
. Once you have A, use 
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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.
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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
,
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First use the 30-60-90 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.
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