WarmUp Honors Algebra 2 41619 3 rd 41719

Warm-Up Honors Algebra 2 4/16/19 3 rd 4/17/19 1 st, 7 th 1. What is the Pythagorean Theorem? 2. What type of triangle is the Pythagorean Theorem used for? 3. What do you use to find the missing adjacent side of a right triangle if you know the angle and the hypotenuse?

Right Triangle Trigonometry:

Relating to the Real World • Before any spacecraft ever traveled to another planet, astronomers had figured out the distance from each planet to the sun. They accomplished this feat by using trigonometry the mathematics of triangle measurement. You will learn how to use trigonometry to measure distances that you could never otherwise measure.

Measure for Measure • What do the Trigonometric Ratios tell you about the parts of a triangle? • What are the conditions for triangles to be similar? • How can you remember the Trigonometric ratios?

Label These Two Triangles Angle A

The Tangent Ratio • The word Trigonometry comes from the Greek words meaning “triangle measurement. ” A ratio of the lengths of sides of a right triangle. This ratio is called the TANGENT. • TANGENT OF A = leg opposite A leg adjacent to A • Slope of a line = Rise Run

Using the Tangent Ratio B • Tangent of < A = Leg OPPOSITE TO < A Leg ADAJACENT TO <A THIS EQUATION CAN BE ABBREVIATED AS: Leg Opposite to < A, BC TAN A = OPPOSITE = BC A C Leg Adjacent to < A, CA ADJACENT CA

Example Write the Tangent Ratios for < U and < T. T Tan U = opposite = TV = 3 adjacent UV 4 5 Tan T = opposite = UV = 4 adjacent TV 3 3 V 4 U

Try This • Write the Tangent ratios for < K and < J • How is Tan K related to the Tan J ? J 3 K L 7

Try This: Find the Tangent of < A to the nearest tenth 1. 2. A 4 8 5 Hint: Find the Ratio First! A 4

Using the Sine Ratio B Leg Opposite to < A, BC • Sine of < A = Leg OPPOSITE TO < A Hypotenuse H yp ot en us e, A B THIS EQUATION CAN BE ABBREVIATED AS: Sin A = OPPOSITE = BC HYPOTENUSE AB A C Leg Opposite to < B, CA Sin B = OPPOSITE = CA HYPOTENUSE AB

Example Write the Sine Ratios for < U and < T. T Sin U = opposite = TV = 3 hypotenuse TU 5 5 Sin T = opposite = UV = 4 hypotenuse TU 5 3 V 4 U

Try This • Write the Sine ratios for < K and < J J 10 6 K L 8

Using the Cosine Ratio B Leg Adjacent to < B, BC • Cosine of < A = Leg Adjacent TO < A Hypotenuse H yp ot en us e, A B THIS EQUATION CAN BE ABBREVIATED AS: Cos A = ADJACENT = CA HYPOTENUSE AB A C Leg Adjacent to < A, CA Cos B = ADJACENT = BC HYPOTENUSE AB

Example Write the Cosine Ratios for < U and < T. T Cos U = adjacent = UV = 4 hypotenuse TU 5 5 Cos T = adjacent = TV = 3 hypotenuse TU 5 3 V 4 U

Try This • Write the Cosine ratios for < K and < J J 10 6 K L 8

Some Old Hippie Came A Hoppin’ Through Our Old Hippie Apartment

Finding a side. (Figuring out which ratio to use and getting to use a trig button. )

Ex: 1 Figure out which ratio to use. Find x. Round to the nearest tenth. 20 m x 20 tan 55 ) Shrink yourself down and stand where the angle is. Now, figure out which trig ratio you have and set up the problem.

Warm-Up Honors Algebra 2 4/17/19 3 rd 4/18/19 1 st, 7 th

Ex: 2 Find the missing side. Round to the nearest tenth. 80 ft x 80 ( tan 72 ) Shrink yourself down and stand where the angle is. Now, figure out which trig ratio you have and set up the problem. ) =

Ex: 3 Find the missing side. Round to the nearest tenth. x 283 m Shrink yourself down and stand where the angle is. Now, figure out which trig ratio you have and set up the problem.

Ex: 4 Find the missing side. Round to the nearest tenth. 20 ft x

Finding an angle. (Figuring out which ratio to use and getting to use the 2 nd button and one of the trig buttons. )

When we are trying to find a side we use sin, cos, or tan. When we are trying to find an angle -1 -1 -1 we use sin , cos , or tan.

Ex. 1: Find . Round to four decimal places. nd 2 17. 2 tan 17. 2 9 9 Shrink yourself down and stand where the angle is. Now, figure out which trig ratio you have and set up the problem. Make sure you are in degree mode (not radians). )