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Transcript of $100 $200 $300 $400 $500 $200 $300 $400 $500 Geometric mean Pythagorean Thm. Special Right Triangles...
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Geometric mean Pythagorean Thm.
Special Right Triangles
Law of Sines and Cosines
TrigonometryAngles of elevation and depression
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Geometric Mean and the Pythagorean Theorem for $100
Solve for b:
12cm
20cmb
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Answer
Pythagorean Theorem: a2 + b2 = c2
122 + b2 = 202
144 + b2 = 400B2 = 256B = 16cm
Back
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Geometric Mean and the Pythagorean Theorem $200
Find the geometric mean between 32 and 2
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Answer
x = √(32*2) = √(64) = 8
Back
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Geometric Mean and the Pythagorean Theorem for $300
List three Pythagorean triples
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Answer
Answers may vary:
3,4,5
6,8,10
5,12,13
20,48,52
Back
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Geometric Mean and the Pythagorean Theorem for $400
Solve for a
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Answer
Back
Based on theorem 7.2, a is the geometric mean of 8 and 6, so
a2 = 8*6
a2 = 48
a = 6.93
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Geometric Mean and the Pythagorean Theorem for $500
In triangle ABC, solve for the length of a
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Based on Theorem 7.3, AC/AB = AB/Ad
So, (29+21)/(a) = (a)/(21)50/a = a/21a2 = 1050a = 32.4
Answer
Back
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Special Right Triangles for $100
Draw and label the sides of a 45-45-90 right Triangle
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Answer
45-45-90 Right Triangle:
Backx
x√(2)x
90° 45°
45°
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Special Right Triangles for $200
Draw and label the sides of a 30-60-90 right Triangle
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Answer
30-60-90 Right Triangle
Backx
2xx√(3)
60°
30°
90°
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Special Right Triangles for $300
If in triangle ABC, AB = 10,
BC = 12 and CA = 9, which angle has the greatest measure?
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Answer
Angle A has the greatest measure because it is opposite side BC, which is the longest side.
Back
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Special Right Triangles for $400
Solve for x and y
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Answer
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Since the triangle is a 30-60-90,
30√(2) = 2y x = y√(3)
y = 15√(2) x = 15√(2)√(3)
x = 15√(6)
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Special Right Triangles for $500
Solve for x and y
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Answer
Back
Since the triangle is a 45-45-90
y = 7 (isosceles triangle so the legs are the same length)
x = 7√(2)
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Trigonometry for $100
List the three basic trigonometry functions and what they equal
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Sin (x) = opposite hypotenuse
Cos (x) = adjacent hypotenuse
Tan (x) = opposite
adjacent
Answer
Back
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Trigonometry for $200
Evaluate:
Sin (30)
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Answer
Back
Sin (30) = 0.5
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Trigonometry for $300
Evaluate cos(x):
15
2520
90° x°
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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
Answer
Back
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Trigonometry for $400
Solve for x:
12
22
90°
x°
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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°
Answer
Back
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Trigonometry for $500
Write the ratios for sin(x) and cos(x)
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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
Answer
Back
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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?
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Answer
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Angle of depression because they are looking down from the horizontal
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Angles of Elevation and Depression for $200
Draw an example of an angle of elevation. Label the angle A
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Answer
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A
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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?
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Answer
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Tan(30) = x/18
18*tan(30) = x
x = 10.4 yds
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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?
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Answer
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tan(5) = x/4629m
4629*tan(5) = x
x = 405m
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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?
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Answer
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140 ft.
x
44°
tan(44) = x/140
140*tan(44) = x
135ft = x
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The Laws of Sines and Cosinesfor $100
Write out the law of sines
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Answer
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The law of sines:
Sin(A) = Sin(B) = Sin(C) a b c
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The Laws of Sines and Cosinesfor $200
Write out the law of cosines
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Answer
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Law of cosines:
A2 = B2 + C2 – 2BC*cos(a)
B2 = A2 + C2 – 2AC*cos(b)
C2 = A2 + B2 – 2AB*cos(c)
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The Laws of Sines and Cosinesfor $300
In triangle ABC, AB = 8, BC = 12 and the m<A = 62 degrees. Solve for m<C.
A 62°
B
C
8 12
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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°
Answer
Back
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The Laws of Sines and Cosinesfor $400
In triangle ABC, AB = 5, BC = 10 and the m<B = 40 degrees. Solve for AC.
A
40°B
5 10
C
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Answer
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B2 = A2 + C2 – 2AC*cos(b)B2 = 102 + 52 – 2(10)(5)*cos(40)B2 = 125 – 100cos(40)B2 = 48.396B = 7
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The Laws of Sines and Cosinesfor $500
In triangle ABC, AB = 8, BC = 6 and the AC = 13. Solve for m<A.
A
B
8 6
C13
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Answer
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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) = aa = 18.7°