Presentation is loading. Please wait.

Presentation is loading. Please wait.

Geometry 9.5 Trigonometric Ratios May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator2 Goals I can find the sine, cosine, and tangent of an acute.

Similar presentations


Presentation on theme: "Geometry 9.5 Trigonometric Ratios May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator2 Goals I can find the sine, cosine, and tangent of an acute."— Presentation transcript:

1

2 Geometry 9.5 Trigonometric Ratios

3 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator2 Goals I can find the sine, cosine, and tangent of an acute angle. I can solve problems using trigonometric ratios.

4 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator3 Terminology No one, uses the word trigonometry. It’s

5 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator4 What is trig? Literally, the measure of triangles. An extremely useful, practical and powerful math tool. A branch of math that finds its way into practically everything we do. Usually learned in high school.

6 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator5 What you will learn… The basic terms and methods of solving right triangles. How to solve problems using trig.

7 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator6 Trig Ratios Based on the sides of a right triangle. We will study only three: Sine Cosine Tangent

8 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator7 Right Triangle Hypotenuse Leg A From  A, this leg is the Adjacent side. From  A, this leg is the Opposite side.

9 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator8 Right Triangle Hypotenuse Leg A From  A, this leg is the Adjacent side. From  A, this leg is the Opposite side. B From  B, this leg is the Adjacent side. From  B, this leg is the Opposite side.

10 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator9 Right Triangle Hypotenuse Adjacent Opposite A

11 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator10 Trig Ratio Definition: Sine Hypotenuse Adjacent Opposite A Sine of  A = Opposite Hypotenuse

12 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator11 Trig Ratio Definition: Cosine Hypotenuse Adjacent Opposite A Cosine of  A = Adjacent Hypotenuse

13 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator12 Trig Ratio Definition: Tangent Hypotenuse Adjacent Opposite A Tangent of  A = Opposite Adjacent

14 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator13 Abbreviations Tangent of  A = Opposite Adjacent Sine of  A = Opposite Hypotenuse Cosine of  A = Adjacent Hypotenuse sin A cos A tan A

15 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator14 Memory Aid Sine is Opposite over Hypotenuse. Cosine is Adjacent over Hypotenuse. Tangent is Opposite over Adjacent. SOHCAHTOA

16 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator15 Writing RatiosSOHCAHTOA A B ? ? ? ? ? ? ? ? ? ? ? ?

17 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator16 Find these values using your calculator—Make sure you’re in Degree Mode!!! SIN 15 COS 45 TAN 45 COS 80 SIN 10 TAN 5 COS 60 SIN

18 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator17 Solving Triangles Carefully analyze what given information you have. Decide what you are trying to find. Ask: how do you use the given information to solve the problem? WRITE AN EQUATION. (SOHCAHTOA) Solve.

19 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator18 Example 1Find x. 28  x 15 From the 28  angle, x is the ? Opposite side, and 15 is the Hypotenuse. What trig ratio is this? Sine (SOHCAHTOA)

20 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator19 Example 1Find x. 28  x 15 Write the equation and solve.

21 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator20 Example 2Find y. 31  y 56 Write the equation and solve.

22 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator21 Example 3Find a. 40  a 8 Write the equation and solve.

23 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator22 Algebra Reminder Solve:

24 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator23 Example 4Find a. 40  a 17 Write the equation and solve.

25 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator24 Example 5Find x & y. 78  xy 150

26 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator25 Angle of Elevation Horizontal Angle of Elevation

27 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator26 Angle of Depression Horizontal Angle of Depression

28 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator27 Problem 30 yd 15  h Standing 30 yards from a tree, the angle of elevation to the top of the tree is 15 . How tall is the tree?

29 May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator28 Summary Trig ratios are based on acute angles in right triangles. They are Sine, Cosine, Tangent. SOHCAHTOA Angle of elevation is from the ground up.


Download ppt "Geometry 9.5 Trigonometric Ratios May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator2 Goals I can find the sine, cosine, and tangent of an acute."

Similar presentations


Ads by Google