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1 Trigonometry Basic Calculations of Angles and Sides of Right Triangles

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2 Use trigonometry to determine the size of an angle.

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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

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

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

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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.

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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...

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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

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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°

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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?

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

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

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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...

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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

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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...

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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.

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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°

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

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

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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...

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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

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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...

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

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

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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...

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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

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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

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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

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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°

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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

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

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

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