Geometry
Test Ch 9
Right Triangle Test
True/False (2 points each)
1. If asked to give an answer in radical form it means to give the answer with a
decimal.
a. true
b. false
2. Pythagorean’s Theorem can be used for all triangles.
a. true
b. false
3. An angle of elevation is the angle formed by a horizontal line and the line of
sight to an object above.
a. true
b. false
4. In a 45-45-90 Triangle the hypotenuse equals the shorter leg times the square
root of 2.
a. true
b. false
5. In a 30-60-90 triangle the length of the hypotenuse is two times the shorter
leg, and the longer leg equals the shorter leg times the square root of 2.
a. true
b. false
Multiple Choice (5 points each)SHOW ALL WORK!!!!
1. Give the side that is the hypotenuse.
x
y
z
a. x
b. y
c. z
d. none
2. Find the value of x. Round to the nearest tenth.
a.
b.
c.
d.
20
8
21.5
18.3
. 21
5.3
x
3. Find the value of y. Round to the nearest tenth.
y
5
13
a. 10.4
b. 14
c. 12
d. 13.9
4. Classify the triangle with sides 6, 9, and 10.
a. Acute
b. Right
c. Obtuse
d. Isosceles
5. Find the area of the triangle in the picture.
6ft
6.71 ft
a.
b.
c.
d.
3 ft2
18 ft2
22.5 ft 2
9 ft2
6. Write the sine ratio of A.
a.
b.
c.
d.
A
5
3
C
B
4
Sin A=4/3
Sin A=3/5
Sin A=4/5
Sin A=3/4
7. In the ratio tan 26 = a/6. The a represents what part of the triangle?
a. leg
b. hypotenuse
c. opposite
d. adjacent
8. If Tan A = 0.268, then mA = ____?
a. 15
b. 0.02
c. 74.5
d. 1
9. Solve for d. sin 52 =
a. 1664
d
32
b. 19.7
c. 25.2
d. 41
10. Solve for the variable. Round to the nearest whole number.
12
8
a
a. 48°
b. 34°
c. 42°
d. 30°
11. Calculate the length of side c.
17
c
70°
a. 47
b. 16
c. 6
d. 24
12. Find the values of each variable.
45°
x
y
3
13. Find the value of b.
a.
b.
c.
d.
x= 3 , y= 3 2
x=6, y=3
x=3 3 , y=3 3
x=3 2 , y=3
30°
b
2 3
a. 2 3
b. 4 2
c. 3
d. 3
60°
14. Find the height of the tree to the nearest foot.
a. 136.1 ft
b. 11 ft
c. 14.7 ft
d. 594 ft
29.7°
20ft
15. An airplane pilot sights a life raft at a 26o angle of depression. The
airplane’s altitude is 3 km. What is the airplane’s surface distance d from
the raft? Round your answer to the nearest whole number.
26°
3 km
d
a. 5km
b. 6km
c. 4km
d. 3km
Open-Response Questions (20 points). Show all work on the grid!!!!!
ORQ 1 Bat
You went to a professional baseball game, and your favorite player
autographed a baseball bat for you. The bat is 34 inches in length. You
want to display the bat in a rectangular case. The case is 28 inches wide, 12
inches deep, and 16 inches high. Can you fit the bat in this case? Explain
your reasoning.
ORQ 2 Ship
A captain of a ship spots the top of a lighthouse at a 47° angle of elevation.
He knows that the lighthouse is 50 ft above the shoreline. How far is the
ship from the shore?
a) Draw and label a picture to represent the lighthouse, shore, and
angle of elevation.
b) Calculate the distance of the ship from the shore.
c) How far would the ship be from the shore if the angle of elevation
was 55°?