Transcript Geometry Jeapordy

Geometric mean
Pythagorean
Thm.
Special Right
Triangles
Trigonometry
Angles of
elevation and
depression
Law of Sines
and Cosines
$100 $100 $100 $100 $100
$200 $200 $200 $200 $200
$300 $300 $300 $300 $300
$400 $400 $400 $400 $400
$500 $500 $500 $500 $500
Geometric Mean and the
Pythagorean Theorem for $100
Solve for b:
20cm
b
12cm
Answer
Pythagorean Theorem:
2
2
2
a +b =c
2
2
2
12 + b = 20
2
144 + b = 400
2
B = 256
B = 16cm
Back
Geometric Mean and the
Pythagorean Theorem $200
Find the geometric
mean between 32 and 2
Answer
x = √(32*2) = √(64) = 8
Back
Geometric Mean and the
Pythagorean Theorem for $300
List three Pythagorean
triples
Answer
Answers may vary:
3,4,5
6,8,10
5,12,13
20,48,52
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Geometric Mean and the
Pythagorean Theorem for $400
Solve for a
Answer
Based on theorem 7.2, a is
the geometric mean of 8 and
6, so
a2 = 8*6
2
a = 48
a = 6.93
Back
Geometric Mean and the
Pythagorean Theorem for $500
In triangle ABC, solve for
the length of a
Answer
Based on Theorem 7.3, AC/AB =
AB/Ad
So, (29+21)/(a) = (a)/(21)
50/a = a/21
a2 = 1050
a = 32.4
Back
Special Right Triangles for $100
Draw and label the sides of
a 45-45-90 right Triangle
Answer
45-45-90 Right Triangle:
45°
x√(2)
90°
45°
x
x
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Special Right Triangles for $200
Draw and label the sides of
a 30-60-90 right Triangle
Answer
30-60-90 Right Triangle
30°
2x
x√(3)
90°
60°
x
Back
Special Right Triangles for $300
If in triangle ABC, AB = 10,
BC = 12 and CA = 9, which
angle has the greatest
measure?
Answer
Angle A has the greatest
measure because it is opposite
side BC, which is the longest
side.
Back
Special Right Triangles for $400
Solve for x and y
Answer
Since the triangle is a 30-60-90,
30√(2) = 2y
x = y√(3)
y = 15√(2)
x = 15√(2)√(3)
x = 15√(6)
Back
Special Right Triangles for $500
Solve for x and y
Answer
Since the triangle is a 45-45-90
y = 7 (isosceles triangle so the
legs are the same length)
x = 7√(2)
Back
Trigonometry for $100
List the three basic
trigonometry functions
and what they equal
Answer
Sin (x) = opposite
hypotenuse
Cos (x) = adjacent
hypotenuse
Tan (x) = opposite
adjacent
Back
Trigonometry for $200
Evaluate:
Sin (30)
Answer
Sin (30) = 0.5
Back
Trigonometry for $300
Evaluate cos(x):
25
20
90°
x°
15
Answer
15 is the adjacent side to x
20 is the side opposite of x
25 is the length of the
hypotenuse
Cos(x) = adjacent/hypotenuse
So, cos(x) = (15/25) = 3/5
Back
Trigonometry for $400
Solve for x:
x°
22
90°
12
Answer
We are given the opposite (12)
and the adjacent (22) sides to
x, so we will use tangent.
Since we are solving for the
angle, we use tan-1
tan-1(12/22) = x
x = 28.6°
Back
Trigonometry for $500
Write the ratios for sin(x)
and cos(x)
Answer
Triangle XYZ is a right triangle, so the trig
functions apply
From angle X,
√(119) is the opposite side
5 is the adjacent side
12 is the hypotenuse
sin(x) = opp/hyp = √(119)/12
cos(x) = adj/hyp = 5/12
Back
Angles of Elevation and
Depression for $100
A person is standing at point A
looking at point B. Does this
represent an angle of elevation
or depression?
Answer
Angle of depression
because they are looking
down from the horizontal
Back
Angles of Elevation and
Depression for $200
Draw an example of an
angle of elevation. Label
the angle A
Answer
A
Back
Angles of Elevation and
Depression for $300
A person stands at the top
of the tower and looks
down at their friend who
is standing 18yds from
the base of the tower. If
the angle of depression is
30 degrees, how tall is the
tower?
Answer
Tan(30) = x/18
18*tan(30) = x
x = 10.4 yds
Back
Angles of Elevation and
Depression for $400
An airplane over the Pacific sights
an atoll at an angle of depression
of 5. At this time, the horizontal
distance from the airplane to the
atoll is 4629 meters. What is the
height of the plane to the nearest
meter?
Answer
tan(5) = x/4629m
4629*tan(5) = x
x = 405m
Back
Angles of Elevation and
Depression for $500
To find the height of a pole, a
surveyor moves 140 feet away
from the base of the pole and
then measures the angle of
elevation to the top of the pole
to be 44. To the nearest foot,
what is the height of the pole?
Answer
x
44°
140 ft.
tan(44) = x/140
140*tan(44) = x
135ft = x
Back
The Laws of Sines and Cosines
for $100
Write out the law of
sines
Answer
The law of sines:
Sin(A) = Sin(B) = Sin(C)
a
b
c
Back
The Laws of Sines and Cosines
for $200
Write out the law of
cosines
Answer
Law of cosines:
A2 = B2 + C2 – 2BC*cos(a)
B2 = A2 + C2 – 2AC*cos(b)
C2 = A2 + B2 – 2AB*cos(c)
Back
The Laws of Sines and Cosines
for $300
In triangle ABC, AB = 8, BC = 12
and the m<A = 62 degrees.
Solve for m<C.
B
8
A
62°
12
C
Answer
Sin(A) = Sin(B) = Sin(C)
a
b
c
Sin(62) = Sin(C)
12
8
8(.0735789661) = sin(c)
sin-1(.5886) = c
c = 36.06°
Back
The Laws of Sines and Cosines
for $400
In triangle ABC, AB = 5, BC = 10 and the
m<B = 40 degrees. Solve for AC.
B
5
A
40°
10
C
Answer
B2 = A2 + C2 – 2AC*cos(b)
B2 = 102 + 52 – 2(10)(5)*cos(40)
B2 = 125 – 100cos(40)
B2 = 48.396
B=7
Back
The Laws of Sines and Cosines
for $500
In triangle ABC, AB = 8, BC = 6 and
the AC = 13. Solve for m<A.
B
8
A
6
13
C
Answer
A2 = B2 + C2 – 2BC*cos(a)
62 = 132 + 82 – 2(13)(8)*cos(a)
36 = 233 – 208cos(a)
-197 = -208cos(a)
0.9471 = cos (a)
cos-1(0.9471) = a
a = 18.7°
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