Idon’t understand numbers 19,20,21 and 22. the question is find the value of each trigonometric ratio to the nearest ten-thousandth.

19) sin 48° ≅ 0.7431

20) sin 38° ≅ 0.6157

21) cos 61° ≅ 0.4848

22) cos 51° ≅ 0.6293

Step-by-step explanation:

* Lets explain the meaning of trigonometry ratio

- In any right angle triangle:

# The side opposite to the right angle is called the hypotenuse

# The other two sides are called the legs of the right angle

* If the name of the triangle is ABC, where B is the right angle

∴ The hypotenuse is AC

∴ AB and BC are the legs of the right angle

- ∠A and ∠C are two acute angles

- For angle A

# sin(A) = opposite/hypotenuse

∴ sin(A) is the ratio between the opposite side of ∠A and the hypotenuse

# cos(A) = adjacent/hypotenuse

∴ cos(A) is the ratio between the adjacent side of ∠A and the hypotenuse

# tan(A) = opposite/adjacent

∴ tan(A) is the ratio between the opposite side of ∠A and the

  adjacent side of A

# The approximation to the nearest ten-thousandth, means look to

  the fifth number before the decimal point if its 5 or greater than 5

  ignore it and add the fourth number (ten-thousandth) by 1 if it is

 smaller than 5 ignore it and keep the fourth number as it

* Now lets solve the problems

19) sin 48° is the ratio between the side opposite to the angle of

    measure 48° and the hypotenuse of the triangle

∴ sin 48° = 0.74314 ≅ 0.7431 ⇒ to the nearest ten-thousandth

20) sin 38° is the ratio between the side opposite to the angle of

    measure 38° and the hypotenuse of the triangle

∴ sin 38° = 0.61566 ≅ 0.6157 ⇒ to the nearest ten-thousandth

21) cos 61° is the ratio between the side adjacent to the angle of

    measure 61° and the hypotenuse of the triangle

∴ cos 61° = 0.48480 ≅ 0.4848 ⇒ to the nearest ten-thousandth

22) cos 51° is the ratio between the side adjacent to the angle of

    measure 51° and the hypotenuse of the triangle

∴ cos 51° = 0.62932 ≅ 0.6293 ⇒ to the nearest ten-thousandth

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step-by-step explanation:

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