Right Triangles and Trigonometry

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Presentation transcript:

Right Triangles and Trigonometry Geometric Mean Pythagorean Theorem Special Right Triangles Trigonometry 100 100 100 100 200 200 200 200 300 300 300 300 400 400 400 400 500 500 500 500

100 Geometric Mean What is Geometric Mean?

The positive square root of two numbers’ product 100 Geometric Mean The positive square root of two numbers’ product

What is the Geometric Mean of 200 What is the Geometric Mean of 4 and 9 ?

Geometric Mean 200

What is the geometric Mean of 300 What is the geometric Mean of 36 and 4

300 Geometric Mean

What is the Geometric Mean of 25 and 9 400 What is the Geometric Mean of 25 and 9

400 Geometric Mean

Is this statement always, sometimes or never true 500 Geometric Mean Is this statement always, sometimes or never true The Geometric Mean for two perfect squares is a positive integer.

500 Geometric Mean Always Why? “The geometric mean between two numbers is the positive square root of their product”

What is the equation for Pythagorean Theorem? 100 Pythagorean Theorem What is the equation for Pythagorean Theorem?

100 Pythagorean Theorem

200 Pythagorean Theorem What is the value of X ? 8 in. 8 in. X 14 in

200 Pythagorean Theorem

300 Pythagorean Theorem

300 Pythagorean Theorem

400 Pythagorean Theorem What is the value of X? 7 in. 14 in. X in.

400 Pythagorean Theorem

Do these three numbers form a Pythagorean Triple? 500 Pythagorean Theorem Do these three numbers form a Pythagorean Triple? 8, 15, 17

500 Pythagorean Theorem 64 + 225 = 289

Special Right Triangles 100 Special Right Triangles X Find X and Y Y* 17 Assume the Shape is a Square

Special Right Triangles 100 Special Right Triangles 2 Y = 45

Special Right Triangles 200 Special Right Triangles Find X and Y 60* 18 X Y

Special Right Triangles 200 Special Right Triangles

Special Right Triangles 300 Special Right Triangles

Special Right Triangles 300 Hypotenuse Long Leg Short Leg

Special Right Triangles 400

Special Right Triangles 400 Leg Hypotenuse

Special Right Triangles 500 Find the value of x X m. X m. 45 * 45 * 6 m.

Special Right Triangles 500

What is the short phrase that can be used as a hint for problems? 100 Trigonometry What is the short phrase that can be used as a hint for problems?

Trigonometry 100 SOH CAH TOA

What does the law of Sines do to find values in a triangle? Trigonometry 200 What does the law of Sines do to find values in a triangle?

Trigonometry 200 Helps to find sides and angles in triangles that are not right triangles but have one complete ratio.

What is the law of Cosines? Trigonometry 300 What is the law of Cosines?

Finds sides and angles with no complete ratio Trigonometry 300 Finds sides and angles with no complete ratio

Trigonometry 400 Find x. Assume it is a right triangle. 17 12 x

Trigonometry 400 X = 44.9

Trigonometry 500 Find x. Assume it is a right triangle 15 18 x

Trigonometry 500 X = 39.8