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Trigonometric Applications: Angle Calculation Practice

Learn to find angle measures of acute right triangles using inverse trig functions. Practice calculating angles from ratios in real-world scenarios. Enhance skills with calculator usage and solve problems like determining heights and angles.

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Trigonometric Applications: Angle Calculation Practice

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

  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

  5. Calculating Inverse Trig Functions • Calculator needs to be in degree mode. • Push 2nd (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) = 38.7º 30º 36.9º • cos-1(.67) = • sin-1(.25) = • cos-1(1/2) = • tan-1(1) = 50.0º 14.5º 60º 45º

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

  8. Real World Example

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

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

  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)

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