Find each angle measure to the nearest degree- pls show work!!

Question

Sin X= 0.7547

sin A= 0.4540

cos Y= 0.5736

cos B= 0.5000

tan B= 0.6239

tan C= 0.1405

Answer 1

X=48.99916333 degrees, use a trig calculator that has inverse functions. That definitely rounds to 49 for nearest degree. Another way to view X is sin45 is a common angle whose sine is sq2/2 = 0.707. .7547 is slightly more than .707, so X is slightly more than 45 degrees. 49 looks about right.

sinA = .4540, A=27.00061091 degrees or 27 rounded off. Use a calculator with an inverse sine function. Also .454 is close to .5. .5 = 1/2 which is the sin30, a common angle in trig. .454 is slightly less than .5, so A is slightly less than 30. 27 looks about right.

cosY= .736 Y=42.60821753 = 43 degrees rounded off. Again, .736 is a little over .707 = sqr2/2, a common right triangle with 45 degrees. 43 is slightly less than 45, and .736 is slightly more than .707 If you drew a picture, a graph, it would make sense.

cosB = 0.5 = 1/2. B = 60 degrees. It's that common right triangle with angles 30-60-90 that you'll see popping up a lot in trigonometry. Almost as common as the 45-45-90 degree right triangle.

tanB=0.6239 B=31.96 = 32 degrees

32 is close to 30. tan30 = 1/sqr3 = 0.577 32 is a little more than 30, so tan32 is a little more than tan30. .6239 is a little more than .577

tanC =.1405. C=7.9977 = 8 degrees

any tangent less than 1 is less than 45 degrees. .1405 is about 1/7 of 1. 1/7 of 45 is about 6 1/2 degrees. 8 degrees is in the right range for the solution. But use a calculator to get the more precise answer

Also each of these answers at a minimum include +n360 where n= any integer.

some have another answer as well. sinX >0 could be in quadrant I or II. a reference angle of 49 degrees in quadrant II is 131 degrees. then add +n360 to that where n= any integer.

There's an infinite number of solutions to each of these problems.

Answer 2

The first one

X = 49°