Answer:
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
