Use the law of cosines to solve ABC with A=126.3, b=45, and c=62.5
I did all the work to find a but my problem is finding B
a=96.2
Sin(B)=45sin126.3/96.2
B=Sin^-1(45sin126.3/96.2)
It's not going through in my calculator
I would use the law of sines to find angle B.
SineB/b=SinA/a
Sin(B)/45=126.3/96.2
im stuck there
B=1.03 and C=52.67
To solve for angle B using the law of cosines, we can use the formula:
cos(B) = (a^2 + c^2 - b^2) / (2 * a * c)
Given that a = 96.2, b = 45, and c = 62.5, we can substitute these values into the formula:
cos(B) = (96.2^2 + 62.5^2 - 45^2) / (2 * 96.2 * 62.5)
Now, we can calculate the right side of the equation:
cos(B) = (9254.44 + 3906.25 - 2025) / (19046 * 62.5)
cos(B) = 12135.69 / 1190625
cos(B) = 0.01019032
To find angle B, we need to take the arccosine of the value we just obtained:
B = arccos(0.01019032)
Now, let's explain how to perform this calculation on a calculator correctly:
Step 1: Make sure your calculator is set to degree mode (°) if you want the angle result in degrees.
Step 2: Enter the value 0.01019032.
Step 3: Press the "arccos" or "cos^-1" button on your calculator.
Step 4: The calculator should give you the value of B, which is approximately 89.834 degrees.
If you encounter any issues with your calculator not giving you the correct value, make sure you have followed the instructions above and that you are using the correct buttons on your calculator. Additionally, check your calculator's user manual for any specific instructions on using trigonometric functions.