# 1 Trigonometry Basic Calculations of Angles and Sides of Right Triangles.

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1 Trigonometry Basic Calculations of Angles and Sides of Right Triangles

2 Use trigonometry to determine the size of an angle.

3 Determine an unknown angle Example 1 To start, we will determine the size of an unknown angle when two sides of the right triangle are known. 5.5” 12” A

4 5.5” 12” A Determine an unknown angle Example 1 Let the unknown angle A be the reference angle.

5 5.5” 12” A opposite adjacent hypotenuse Determine an unknown angle Example 1 Now label the sides of the right triangle...

6 5.5” 12” A opposite adjacent hypotenuse Determine an unknown angle Example 1 Note that we only know the lengths of the opposite and adjacent sides.

7 5.5” 12” A opposite adjacent Determine an unknown angle Example 1 So we need to pick a trig function that has the opposite and adjacent sides in it...

8 Determine an unknown angle Example 1 Which trig function should you pick? You need to pick the tangent function since it is the only one that has both opposite and adjacent sides in it. 5.5” 12” A opposite adjacent

9 5.5” 12” A opposite adjacent Now use your calculator to solve. Type-in.458333, press the 2nd function key, then press the tan key Determine an unknown angle Example 1 Now plug-in the numbers you have into the tangent function... A = 24.6°

10 5.5” 12” 24.6° This angle is 90°…..and this one was computed to be 24.6°… …this one must be 65.4° degrees. (Since 180° - 90° - 24.6° = 65.4°) 65.4° Determine an unknown angle Example 1 How could you determine the size of the remaining angle?

11 Determine an unknown angle Example 2 Let’s try another one… Determine the size of angle A. 35 mm 31.5 mm A

12 35 mm 31.5 mm A opposite adjacent hypotenuse Determine an unknown angle Example 2 First, label the sides of the triangle...

13 35 mm 31.5 mm A adjacent hypotenuse Determine an unknown angle Example 2 Since you know the lengths of the adjacent side and the hypotenuse, pick a trig function that has both of these...

14 You need to pick the cosine function since it is the only one that has both the adjacent side and hypotenuse in it. Determine an unknown angle Example 2 Which trig function should you pick? 35 mm 31.5 mm A adjacent hypotenuse

15 35 mm 31.5 mm A adjacent hypotenuse Now use your calculator to solve. Type-in 0.9, press the 2nd function key, then press the cos key Determine an unknown angle Example 2 Now plug-in the numbers you have into the cosine function...

16 35 mm 31.5 mm 25.8° Determine an unknown angle Example 2 Now that you know how big angle A is, determine the size of the remaining angle.

17 35 mm 31.5 mm 25.8° 64.2° Determine an unknown angle Example 2 To determine the other angle: 180° - 90° - 25.8° = 64.2°

18 Determine an unknown angle Example 3 Let’s try one more. Determine the size of angle A. A 125 mm 132 mm

19 A 125 mm 132 mm opposite hypotenuse adjacent Determine an unknown angle Example 3 Label the sides of the triangle...

20 A 125 mm 132 mm opposite hypotenuse Determine an unknown angle Example 3 Since you know the lengths of the opposite side and the hypotenuse, pick a trig function that contains them...

21 You need to pick the sine function since it is the only one that has both the opposite side and hypotenuse in it. Determine an unknown angle Example 3 Which trig function should you pick? A 125 mm 132 mm opposite hypotenuse

22 A 125 mm 132 mm opposite hypotenuse Now use your calculator to solve. Type-in 0.947, press the 2nd function key, then press the sin key Determine an unknown angle Example 3 Now plug-in the numbers you have into the sine function...

23 71.3° 125 mm 132 mm Determine an unknown angle Example 3 What is the size of the remaining angle?

24 71.3° 125 mm 132 mm 18.7° Determine an unknown angle Example 3 The angle is computed to be 18.7°.

25 Summary of Part II By now you should feel like you have a pretty good chance of determining the size of an angle when any two sides of a right triangle are known. Click to see one more problem like the last three you have done...

26 Summary of Part II Example 4 Determine the size of angle A. Solve the problem, then click to see the answer. A 25.5 ft 23 ft

27 A 25.5 ft 23 ft Summary of Part II Example 4 Selecting the cos function will allow you to determine the size of angle A. adjacent hypotenuse

28 Summary After viewing this lesson you should be able to: –Compute an interior angle in a right triangle when the lengths of two sides are known. 5.25” 8.75” x

29 Summary After viewing this lesson you should be able to: –Compute the length of any side of a right triangle as long as you know the length of one side and an acute interior angle. 7.5” x 60°

30 Final Practice Problem Example 10 Determine the lengths of sides x and y and the size of angle A. When you are done, click to see the answers on the next screen. 15° A 85 cm x y

31 Final Practice Problem Example 10 The answers are shown below... 15° 75° 85 cm 88 cm 22.8 cm

32 Homework pg. 485 #3 pg. 486 #7, 10,12,14,19,20

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