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2. For parts (a)–(c), find the value of w to the nearest tenth.

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   2. 
   3. 
   4. A section of Filbert Street in San Francisco rises at an angle of about 17 ° . 17 degrees . If you walk 150 ft up this section, what is your vertical rise? Round to the nearest foot.

Problem 3 Using Inverses

What is m ∠ X m angle x to the nearest degree?

1. 
   You know the lengths of the hypotenuse and the side opposite ∠ X . angle x .
   Use the sine ratio.
   sin   X = 6 10 Write the ratio . m ∠ X = sin − 1 ( 6 10 ) Use the inverse . sin − 1 6 ÷ 10 enter Use a calculator . m ∠ X ≈ 36.86989765     ≈ 37   table with 5 rows and 3 columns , row1 column 1 , sine x , column 2 equals , 6 tenths , column 3 cap writetheratio . . , row2 column 1 , m angle x , column 2 equals . sine super negative 1 end super . open , 6 tenths , close , column 3 cap usetheinverse . . , row3 column 1 , begin box , sine super negative 1 end super , end box , column 2 6 begin box , divides , end box 10 , begin box , enter , end box , column 3 cap useacalculator . . , row4 column 1 , m angle x , column 2 almost equal to . 36.86989765 , column 3 , row5 column 1 , , column 2 almost equal to 37 , column 3 , end table

2. 

   You know the lengths of the hypotenuse and the side adjacent to ∠ X . angle x .

   Use the cosine ratio.

   cos  X = 15 20 m ∠ X = cos − 1 ( 15 20 ) cos − 1 15 ÷ 20 enter m ∠ X ≈ 41.40962211   ≈ 41 table with 5 rows and 2 columns , row1 column 1 , cos x , column 2 equals , 15 over 20 , row2 column 1 , m angle x , column 2 equals . cosine super negative 1 end super . open , 15 over 20 , close , row3 column 1 , begin box , cosine super negative 1 end super , end box , column 2 15 begin box , divides , end box 20 , begin box , enter , end box , row4 column 1 , m angle x , column 2 almost equal to . 41.40962211 , row5 column 1 , , column 2 almost equal to 41 , end table

✓ Got It?

3. 1. Use the figure below. What is m ∠ Y m angle y to the nearest degree?

      
   2. Reasoning Suppose you know the lengths of all three sides of a right triangle. Does it matter which trigonometric ratio you use to find the measure of any of the three angles? Explain.