Transcript Chapter 9 test 2

Chapter 9 test 2
answers
• 1. The HYPOTENUSE is the side opposite the
right angle in a right triangle.
• 2. In a right triangle, if x and y are the lengths of
the legs and z is the length of the hypotenuse,
then _x2 + y2 = z2__ (formula).
• 3. In an isosceles right triangle, if the
hypotenuse has length x, then each leg has
length _x/√2___.
• 4. In a 30-60-90 triangle, if the hypotenuse has
length y, then the shorter leg has length
__y/2___ and the longer leg has length
__y√3/2___.
5. Determine whether ABC with vertices A(2, 4),
B(10, 2), and C(7, 7) is scalene, isosceles, or
equilateral.
a 2 + b 2 = c2
A( 2, 4)
A( 2, 4)
C( 7, 7)
B(10, 2)
C( 7, 7)
B(10, 2)
82 + 22 = c2
52 + 32 = c2
3 2 + 52 = c 2
64 + 4 = c2
25 + 9 = c2
9 + 25 = c2
68 = c2
34 = c2
34 = c2
√68 = c
√34 = c
√34 = c
isosceles
6. A jet flies under another at midnight. The lower jet is
traveling south at 300 km/hr at an altitude of 12,500
feet; the other is traveling east at 400 km/hr at an
altitude of 15,500. If they continue on their current
flight paths, without varying their altitude or speed,
how far apart will they be in 3 hours?
a2 + b2 = c2
(300 • 3)2 + (400 • 3)2 = c2
9002 + 12002 = c2
810000 + 1440000 = c2
2250000 = c2
1500 = c
1500 km apart
7.Find the area of an
equilateral triangle with
sides measuring 8 meters.
bh
2
4 • 4√3
16√3
16√3 m2 or 27.71 m2
8 4√3 8
4
8 4
8. To the nearest foot, find the original height of a fallen flagpole
that cracked and fell as if hinged, forming an angle of 45 with
the ground where it hit. The tip of the pole hit the ground 12
feet from its base which is still standing upright.
12 feet
Since this is an isosceles right triangle, the two
legs (the ground and the remaining upright
portion of the flag pole are both 12 feet and the
hypotenuse is 12√2.
12 + 12√2 = original height of flagpole
45º
12 + 12 • 1.4
12 + 16.8
28.8 feet
The original height of the
90º
45º
Flagpole was 28.8 feet.
12 feet
Chapter 10 test 1
answers
1.The EDGES of a prism are the line segments
where the lateral faces intersect.
2.A SPHERE is the set of all points at a given
distance from a given point.
3.The altitude of a pyramid is a
PERPENDICULAR segment from the
VERTEX to the plane of the base.
4.An object’s density is calculated by dividing
the MASS of the object by its VOLUME.
5. A scoop of ice cream, shaped like a sphere with a diameter 6 cm,
is placed in an ice cream cone with diameter 5 cm and height 10 cm.
Is the cone big enough to hold all the ice cream if it melts? Explain.
Sphere
4πr3
3
4 • 3.14 • 3 • 3 • 3
3
113.04 cm3
>
Cone
πr2H
3
3.14 • 3 • 3 • 10
3
94.2 cm3
When the ice cream melts, it will over runneth the cone.
6. Which container would hold more popcorn: a can
cylinder with a diameter of 7 inches and a height of 7
inches or a cardboard box that measures 7 inches on
each edge?
Cylinder
πr2H
3.14 • 3.5 • 3.5 • 7
269.225 in3
<
Prism
bhH
7•7•7
343 in3
The cardboard box can hold more
popcorn.
7. What are the smallest measurements [B (b and h)
and H] would a pyramid have to have to hold the
same amount of sand as a cone with a base radius of
3 inches and a height of 8 inches?
Pyramid
Cone
The
bhH
πr2H
dimensions for
3 3
3
the pyramid
3.14 • 9 • 8
3.14 • 3 • 3 • 8
could be
3
3
B = 3.14 • 9
3
3
99.36
in
99.36 in
and H = 8
8. p. 537 # 9
D = m/v
3088 g
10 • 10 • 1.6 cm3
3088 g
160 cm3
D = 19.3 g/cm3
The medallion is gold and Colonel
Banderson is whom he says he is.