1. Warm Up If name is on the board put HW on the board Complete the warm up on the board with a partner. Section 8.3

2. Objectives  To find the angle measures of acute right triangles using the inverse trig functions with real world applications

3. Calculating Angles from Ratios  In the previous power point we learned how to find a side length give an angle and a sine, cos or tan ratio.  Now we will use the same ratio to find the given angle by using an inverse function.

4. Inverse Trigonometric Functions If sinA = x, then sin -1 x = mA If cosA = x, then cos -1 x = mA If tanA = x, then tan -1 x = mA

5. Calculating Inverse Trig Functions  Calculator needs to be in degree mode.  Push 2 nd (sin, cos or tan)  Type in ratio (This should be in fraction form).  Press Enter  You how have angle, round if necessary.

6. Practice  Use calculator to solve: (Round to nearest tenth) tan -1 (4/5) = sin -1 (1/2) = cos -1 (4/5) = 50.0º 14.5º 60º 45º cos -1 (.67) = sin -1 (.25) = cos -1 (1/2) = tan -1 (1) = 38.7º 30º 36.9º

7. Practice Continued 10 12 x° 17 5 y° 6 12 z° x =50.2º y =17.1º z =60º

8. Real World Example

9. Water Heater Problem # 1 Determine the Height of the Water Heater to the nearest foot. Water Heater Myth Busters 100 ft 67° Tan 67º = x/100 2.356 = x/100 235.6 = x 236 ft = x

10. Water Heater Problem # 2 Determine the Angle of elevation between the ground and the path between MB & WH to the nearest degree. Water Heater 300ft Myth Busters 100 ft x° Tan -1 x = 300/100 Tan-1 x = 3 x = 71.5º x = 72º

11. Follow-Up  Practice the following worksheet on Trig functions on your own and we will put them on the board.  Homework: Worksheet B (8.3)