Download Geo-Ch09-Test

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Chapter 9 Test- Advanced Geometry
Name: ______________________________
Period: ________ Date: _______________
Please show all work when necessary. Circle or box the correct response.
1.
2.
If the side lengths of a triangle are 7, 8, and 10, the triangle
_____
[A] is an obtuse triangle
[B] is a right triangle
[C] is an acute triangle
[D] cannot be formed
What is cosA.?
_____
(3 pts).
(3 pts)
B
17
15
A
[A]
3.
8
C
8
15
[B]
[C]
15
17
[D]
8
17
Assume that A is an acute angle and tanA = 0.6307. The measure of A is _____.
(3 pts)
[A]  29.9°
4.
15
8
[B]  32.2°
Solve for x to the nearest degree.
[C]  39.1°
[D]  59.1°
_____
(3 pts)
6
x°
[A] 23
14
[B] 45
[C] 65
[D] 76
Advanced Geometry
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Please show all work. A correct response with no supporting work will receive 1 point.
Simplify all fractions and radicals. Please give exact answers or round to the nearest
hundredth.
5.
Find the altitude of an isosceles triangle with base 14 cm and congruent sides of length 8
cm.
(4 pts)
6.
What is the length of a side of a square with a diagonal of length 8 cm? (You must leave
your answer as a simplified radical.)
(4 pts)
7.
What is the area of an equilateral triangle with side lengths of 12 m?
8.
A slide 6.5 m long makes an angle of 35° with the ground. How high is the top of the slide
above the ground?
(4 pts)
(4 pts)
Advanced Geometry
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Solve the right triangle. Given:   55 and b = 15 in.; find  , a, and c
9.

c
(7 pts)
b

a
10.
Find all reasonable values for x if TVU  90 and VW is the altitude of TVU .
(7 pts)
V
3x
T
11.
2x
W
4x+3
U
On the problem #10 above, what would be a correct similarity statement of 2 right triangles
among 3?
_____
(3 pts)
[A] TVU TVW
[B] TVU VWU
[C] TVU UWV
[D] VWT TVU
Advanced Geometry
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12.
An antenna is atop the roof of a 120-foot building, 10 feet from the edge, as shown in the
figure below. From a point 50 feet from the base of the building, the angle from ground
level to the top of the antenna is 66°. Find x, the length of the antenna, to the nearest foot.
(Hint: The triangles are not similar. The edge of 10 ft. part does not intersect the dashed
diagonal.)
(6 pts)
x
10 ft
66 °
50 ft
For the open-ended section, you must show work to receive full/partial credit. A correct
response without supporting algebraic work will receive 1 point. Simplify all fractions and
radicals. Please give exact answers or round to the nearest hundredth.
13.
Use the graph to sketch the diagram. Answer all parts.
a) Plot and label the following points. A(5, 0), B(5, -2), C(10, -2), D(5, 4) and E(-5, 4).
(5 pts)
Advanced Geometry
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b) Find the slopes of the following lines algebraically:
(4 pts)
ED: __________
DB: __________
c) Find the lengths of the following sides of a triangle. Show work when necessary (AC
with distance formula).
(5 pts)
AB = ______
AC = ______
BC = ______
d) Is triangle ABC a right triangle? Justify your reasoning.
(4 pts)
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
e) Find the measures of the following angles to the nearest tenth. You need to show work
when necessary, or justify your reasoning in calculating the angle measures. (6 pts)
work/reasoning
work/reasoning
mACB 
mEAD 
f) Are the triangles congruent, similar, or neither? Justify your reasoning.
(4 pts)
Advanced Geometry
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14.
The given vector represents the velocity of a ship at sea, where each unit is 10 miles/hr.
a) Write the vector in component form.
(3 pts)
b) Find the ship’s speed (magnitude), rounded to the nearest mile per hour. (4 pts)
c) Find the direction the ship is traveling relative to east.
15.
(a) Find the value of x and y to the nearest tenth.
(4 pts)
(6 pts)
A
18
x
50
B
30
D
y
C
(b) Find the area of the triangle to the nearest tenth.
(4 pts)
Advanced Geometry