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Geometric mean Pythagorean Thm.

Special Right Triangles

Law of Sines and Cosines

TrigonometryAngles of elevation and depression

Geometric Mean and the Pythagorean Theorem for $100

Solve for b:

12cm

20cmb

Answer

Pythagorean Theorem: a2 + b2 = c2

122 + b2 = 202

144 + b2 = 400B2 = 256B = 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

Back

Geometric Mean and the Pythagorean Theorem for $400

Solve for a

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

Geometric Mean and the Pythagorean Theorem for $500

In triangle ABC, solve for the length of a

Based on Theorem 7.3, AC/AB = AB/Ad

So, (29+21)/(a) = (a)/(21)50/a = a/21a2 = 1050a = 32.4

Answer

Back

Special Right Triangles for $100

Draw and label the sides of a 45-45-90 right Triangle

Answer

45-45-90 Right Triangle:

Backx

x√(2)x

90° 45°

45°

Special Right Triangles for $200

Draw and label the sides of a 30-60-90 right Triangle

Answer

30-60-90 Right Triangle

Backx

2xx√(3)

60°

30°

90°

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

Back

Since the triangle is a 30-60-90,

30√(2) = 2y x = y√(3)

y = 15√(2) x = 15√(2)√(3)

x = 15√(6)

Special Right Triangles for $500

Solve for x and y

Answer

Back

Since the triangle is a 45-45-90

y = 7 (isosceles triangle so the legs are the same length)

x = 7√(2)

Trigonometry for $100

List the three basic trigonometry functions and what they equal

Sin (x) = opposite hypotenuse

Cos (x) = adjacent hypotenuse

Tan (x) = opposite

adjacent

Answer

Back

Trigonometry for $200

Evaluate:

Sin (30)

Answer

Back

Sin (30) = 0.5

Trigonometry for $300

Evaluate cos(x):

15

2520

90° x°

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

Trigonometry for $400

Solve for x:

12

22

90°

x°

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

Trigonometry for $500

Write the ratios for sin(x) and cos(x)

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

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

Back

Angle of depression because they are looking down from the horizontal

Angles of Elevation and Depression for $200

Draw an example of an angle of elevation. Label the angle A

Answer

Back

A

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

Back

Tan(30) = x/18

18*tan(30) = x

x = 10.4 yds

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

Back

tan(5) = x/4629m

4629*tan(5) = x

x = 405m

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

Back

140 ft.

x

44°

tan(44) = x/140

140*tan(44) = x

135ft = x

The Laws of Sines and Cosinesfor $100

Write out the law of sines

Answer

Back

The law of sines:

Sin(A) = Sin(B) = Sin(C) a b c

The Laws of Sines and Cosinesfor $200

Write out the law of cosines

Answer

Back

Law of cosines:

A2 = B2 + C2 – 2BC*cos(a)

B2 = A2 + C2 – 2AC*cos(b)

C2 = A2 + B2 – 2AB*cos(c)

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

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

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

Answer

Back

B2 = A2 + C2 – 2AC*cos(b)B2 = 102 + 52 – 2(10)(5)*cos(40)B2 = 125 – 100cos(40)B2 = 48.396B = 7

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

Answer

Back

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°