Use the law of sines
Find a side of any triangle when you know the opposite angle of another side and its length.
In any triangle, side ÷ sin(opposite angle) is the same for all three sides. So a ÷ sin A = b ÷ sin B.
Example: a = 10, A = 30 degrees and B = 45 degrees. Then b = 10 × sin 45 ÷ sin 30 = 14.14213562.
Classic Graphing 84
Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.
Switch to degree mode.
mode▼▼▶enter2ndQUITmodeType 10 × sin(45) ÷ sin(30) and press enter.
10×sin45)÷sin30)enter
You should see14.14213562
Classic Scientific 30
Start on the main screen: Press 2nd then mode (QUIT) to leave any menu or screen and return to the calculation screen.
Type the same formula. The answer is exact (10√2).
10×sin45)÷sin30)enterPress the ◄► key to switch to the decimal.
◄►
You should see14.14213562
Natural Scientific 991
Start on the main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on.
The calculator starts in degrees. Type 10 × sin(45) ÷ sin(30) and press =.
10×sin45)÷sin30)=The exact answer is 10√2. Press S⇔D for the decimal.
S⇔D
You should see14.14213562
Natural Color Graphing
Start on the main screen: Press MENU then 1 to open Run-Matrix, the main calculation screen. Press EXIT to back out of a bar or screen, and SHIFT then EXIT (QUIT) to return to the app start.
Set degrees and type the formula.
SHIFTSET UPMENU▼▼F2EXIT10×sin45)÷sin30)EXEPress S⇔D to change 10√2 into a decimal.
S⇔D
You should see14.14213562
Classic CAS
Start on the main screen: Press home to open the Home menu (Calculator, Graphs, Settings, and more). Choose Calculator, or press esc to go back to the calculation page.
Set degrees, then type the formula. Use ctrl enter to get a decimal.
menu9▼▶enterenterenter10×sin45)÷sin30)ctrl≈enter
You should see14.1421
RPN Scientific 15
Start on the main screen: There is no menu to leave. Press the back arrow to clear a number you are typing, or CLx (g then back arrow) to clear the X register.
Key in 10 ENTER, then 45 SIN ×.
10ENTER45SIN×Key in 30 SIN and press ÷.
30SIN÷
You should see14.1421
RPN Advanced 42
Start on the main screen: Press EXIT (once or twice) to close any menu and return to the plain stack view of Y and X.
Key in 10 ENTER, 45 SIN ×, then 30 SIN ÷.
10ENTER45SIN×30SIN÷
You should seex: 14.1421
RPN Power 48
Start on the main screen: Press ON to cancel what you are typing, then use the stack view. Open the MODE or VAR menu any time; the stack is always shown above the menu row.
Choose DEG on the MODE menu, then enter 10 ENTER 45 SIN × 30 SIN ÷.
MODEF510ENTER45SIN×30SIN÷
You should see14.1421356237
Tips
- Use the law of sines when you have a side and its opposite angle. If you have two sides and the angle between them, use the law of cosines instead.
- Given two sides and a non-included angle, there can be two answers. The triangle solver tool shows both.
Related guides
- Use the law of cosinesFind the third side of a triangle when you know two sides and the angle between them.
- Solve any triangle with the solver toolUse the Triangle solver in the Reference library when you know three parts of a triangle and want the rest, drawn to scale.
- Solve a right triangleFind a missing side from the hypotenuse and an angle, and a missing angle from two sides.