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Geometry
Unit 7 Review
Name ______________________
Write each radical in simplest form.
1)
4)
72
10
3
2)
5)
3) 3 75
12
12
6
6)
5
6
Solve for the unknown side. Round answers to the nearest tenth.
Use the Pythagorean Theorem
c 2 ____ a 2  b2 for a right triangle with 1 unknown side
7)
8)
Determine if the set of numbers could represent the sides of a triangle. If so, what type
of triangle? Show work!!
To make a triangle, any 2 sides summed must be _____________ than the third side
Then compare
9)
29, 32, 17
12)
2, 3, 6
c 2 ____ a 2  b2 to determine which kind of triangle.
10)
13)
14, 15, 28
11)
15, 25, 20
9, 15, 10 3
14)
7, 5, 4
Find the value of the variable. Answers should be simplified radicals.
Draw the small, medium, and large SIMILAR triangles and set up proportions OR…
Use the Geometric Mean Theorem (length of altitude = geo. Mean of 2 parts of hyp.)
15)
16)
17)
26
18
12
12
x
y
2
y
4
Find the unknowns for each triangle. Answers should be simplified radicals.
(triangles not drawn to scale)
These are special right triangles.
18.
19.
20.
x
y
7 2
30
y
y
x
45
45
5
x
6
x = ______
y = ______
x = ______
y = ______
x = ______
y = ______
21.
30
22.
30
23.
12
x
y
2 3
30
x
x = ______
24.
y = ______
x = ______
y = ______
x = ______
25.
60
x = ______
x
y
x
4 2
7 3
y
y
y = ______
y
6
30
x = ______
x
y = ______
y = ______
Find the value of the variable(s). Round all answers to the nearest tenth. SHOW ALL WORK!
Trig Problems! First step is to pick an angle and ______________ the triangle.
You need to memorize
S
O
H
C
A
H
T
O
A
Remember, use _________ trig functions when finding an angle.
26.
27.
28.
10
18
x
21
x
36
x = ______
29.
66
8
x
x = ______
30.
x = ______
31.
18
15
10
x
x
30
x
28
33
y
x = ______
x = ______
x = ______
y = ______
4
32.
33.
z
x
20
10
55°
x
y
x = ______
y = ______ z = _______
x = ______
Application and Word Problems
Use what you know about right triangles to solve the problem. Think about when you
can use the Pythagorean Theorem, Trig, or Special Right Triangle patterns.
34)
16
35) The perimeter of the rectangle is 40 inches.
Find the length of the diagonal, x.
12
13
x
15
x
x = ______
x = ______ (round to tenth place)
36) Find the area of the triangle
20 in
Area = _______
25 in
If no picture is provided, SKETCH AND LABEL A DIAGRAM!
37)
If a TV screen is a rectangle with a 53-inch diagonal and a width of 45 inches, what
is the height of the TV screen?
38)
A 30-foot ladder is placed against a vertical wall so that the base of the ladder is 10 feet from
the base of the wall. How far up the wall does the ladder reach AND what angle does the ladder
make with the floor?
39) The perimeter of an equilateral triangle is 45 inches. What is the area of the triangle?
40)
The legs of a right triangle are 3 and 4 cm. Find, to the nearest whole degree, the measure
of the LARGER acute angle in the triangle.
41)
A straight road from the base to the top of a hill makes an angle of 12° with the
horizontal. If the hill has an altitude of 520 m, find the length of the road, rounded to the
nearest whole meter.
42)
A child 90 cm high casts a shadow that is 180 cm long. Find the angle of elevation to the sun,
Rounded to the nearest whole degree.