Find A, given that a = 18.2, B = 62, and C = 48. Round answers to the nearest whole degree. Do not use a decimal point or extra spaces in the answer or it will be marked incorrect.
I assume A is an angle of a triangle with given sides. Recall your law of cosines:
a^2 = b^2 + c^2 - 2bc*cosA
331.24 = 3844 + 2304 - 5952 cosA
cosA = 0.97727
A = 12.237°
To find the value of A, we can use the sine rule which states that for any triangle:
a/sin(A) = b/sin(B) = c/sin(C)
Given that a = 18.2, B = 62, and C = 48, we can substitute these values into the sine rule equation:
18.2/sin(A) = 62/sin(62) = 48/sin(48)
To isolate sin(A), we rearrange the equation:
sin(A) = 18.2 / (62 / sin(62))
sin(A) ≈ 18.2 / (0.8837)
sin(A) ≈ 20.61
Now, to find the value of A, we can use the arcsin function (also known as inverse sine) which gives us the angle whose sine is a given value. In this case, we want to find A, so we input the value of sin(A) which is approximately 20.61:
A ≈ arcsin(20.61)
Using a calculator, we find that arcsin(20.61) is approximately 89.9 degrees.
Rounding this value to the nearest whole degree, we get A ≈ 90 degrees.