Download 1) The area of a square is 10 square centimeters. What is

Mathematics IIA
Right Triangle Trigonometry Unit
Review
Name ________________________________
Date _____________________ Period _____
MM2G1. Students will identify and use special right triangles.
MM2G1a. Determine the lengths of sides of 30°-60°-90° triangles.
MM2G1b. Determine the lengths of sides of 45°-45°-90° triangles.
1) The area of a square is 10 square
centimeters. What is the product
of the lengths of the diagonals of
the square?
2) A parallelogram has sides that are
10 cm and 20 cm long. The
measure of the acute angles of the
parallelogram is 30°. What is the
area of the parallelogram?
3) What is the area of a regular
4) The length of one diagonal of a
hexagon with sides that are 10 cm
rhombus is 12 cm. The measure
long?
of the angle opposite that
diagonal is 60º. What is the
perimeter of the rhombus?
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Mathematics IIA
Right Triangle Trigonometry Unit
Review
5) Quadrilateral LMTP is an
isosceles trapezoid. What is the
length of LP?
6) A rhombus is show below. If the
height, h, intersects the base at its
midpoint, what is the height of
the rhombus?
7) A right triangle is shown below.
What is the approximate value of
h?
8) What is the closest value of t for
the triangle with the dimension
shown below?
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Mathematics IIA
Right Triangle Trigonometry Unit
Review
MM2G2. Students will define and apply sine, cosine, and tangent ratios to right triangles.
MM2G2a. Discover the relationship of the trigonometric ratios for similar triangles.
MM2G2b. Explain the relationship between the trigonometric ratios of complementary angles.
9) Angle J and angle K are
complementary angles in a right
triangle. The value of tan J is .
What is the value of sin J?
Triangle RST is a right triangle
with right angle S, as shown.
What is the area of triangle RST?
10) ̅̅̅̅̅ is an altitude of
, and
̅̅̅̅̅ ̅̅̅̅. The measure of
is
, and
. What is the approximate
length of ̅̅̅?
From a point 12 feet from the
base of a building, the angle of
elevation from the ground to the
top of the building is
. What is
the height of the building?
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Mathematics IIA
Right Triangle Trigonometry Unit
Review
MM2G2. Students will define and apply sine, cosine, and tangent ratios to right triangles.
MM2G2c. Solve application problems using the trigonometric ratios.
A road ascends a hill at an angle
of 15°. For every 100 feet of
road, how many feet does the
road ascend?
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According to building codes, the
maximum angle of ascent for a
staircase in a home is 42.5°. To
get from the first floor to the
second floor in a new home, a
staircase will have a total vertical
distance of 115.5 inches. What is
the minimum horizontal distance,
to the nearest inch, needed for the
staircase?
Mathematics IIA
Right Triangle Trigonometry Unit
Review
Bianca uses an angle-measuring
device on a 3-foot tripod to find
the height, h, of a weather balloon
above ground level, as shown in
this diagram. The balloon is at a
40° angle of elevation. A radio
signal from the balloon tells
Bianca that the distance between
the tripod and the balloon is
25,000 feet.
Write an expression to represent
the height, h, of the balloon above
ground level?
11) Use this diagram of a cone to answer the question.
The base of the cone has a radius
of 6 cm. Which expression
represents the slant height, in
centimeters, of the cone?
What is the volume of the cone?
(remember: V = 1/3 bh)
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Mathematics IIA
Right Triangle Trigonometry Unit
Review
12) A dead tree was struck by lightning, causing it to
fall over at a point 10 up from its base. If the fallen
treetop forms a
angle with the ground, about
how tall was the tree originally?
13) A ladder is leaning against the side of a building.
The ladder is 30 feet long, and the angle between
the ladder and the building is
. About how far
is the foot of the ladder from the building?
14) The angle of elevation from point G on the ground
to the top of a flagpole is
. The height of the
flagpole is 60 feet. Write the equation to find the
distance from point G to the base of the flagpole.
15) The diagram below shows the side view of a
house. The base of its roof is 4 meters above
ground level. Point P is the highest point on the
roof. Based on the diagram, what is the distance
from P to the ground level?
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