Solve a right triangle
Find a missing side from the hypotenuse and an angle, and a missing angle from two sides.
Say the hypotenuse is 10 and one angle is 35 degrees. The side opposite that angle is 10 × sin 35, which is 5.735764364.
To find an angle from two sides, use an inverse function. If the opposite side is 3 and the adjacent side is 4, the angle is tan⁻¹(3 ÷ 4) = 36.86989765 degrees.
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▼▼▶enter2ndQUITmodeOpposite side: 10 × sin(35).
10×sin35)enterAngle: tan⁻¹(3 ÷ 4).
2ndtan⁻¹tan3÷4)enter
You should see5.735764364 36.86989765
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.
This model starts in degrees. Opposite side: 10 × sin(35).
10×sin35)enterAngle: tan⁻¹(3 ÷ 4), using 2nd then tan.
2ndtan⁻¹tan3÷4)enter
You should see36.86989765
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.
This model starts in degrees. Opposite side: 10 × sin(35).
10×sin35)=Angle: SHIFT then tan, then the fraction 3 over 4. Press the right arrow to leave the fraction before =.
SHIFTtan⁻¹tan3/4▶=
You should see36.86989765
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, then work out the opposite side.
SHIFTSET UPMENU▼▼F2EXIT10×sin35)EXEAngle: SHIFT then tan with the fraction 3 over 4.
SHIFTtan⁻¹tan3/4▶EXE
You should see5.735764364 36.86989765
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. Opposite side: 10 × sin(35), with ctrl enter for a decimal.
menu9▼▶enterenterenter10×sin35)ctrl≈enterAngle: ctrl tan for tan⁻¹, then 3 ÷ 4.
ctrltan⁻¹tan3÷4)ctrl≈enter
You should see5.73576 36.8699
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.
Opposite side: 10 ENTER 35 SIN ×.
10ENTER35SIN×Angle: 3 ENTER 4 ÷, then g TAN for the inverse tangent.
3ENTER4÷gTAN⁻¹TAN
You should see5.7358 36.8699
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.
Opposite side: 10 ENTER 35 SIN ×.
10ENTER35SIN×Angle: 3 ENTER 4 ÷, then shift TAN.
3ENTER4÷⇧ATANTAN
You should seey: 5.7358 x: 36.8699
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. Opposite side: 10 ENTER 35 SIN ×.
MODEF510ENTER35SIN×Angle: 3 ENTER 4 ÷, then left shift TAN.
3ENTER4÷◀ATANTAN
You should see5.73576436351 36.8698976458
Tips
- Label the triangle first: which side is opposite your angle, which is adjacent, and which is the hypotenuse? Then pick sin, cos or tan to match.
- A missing side opposite = hypotenuse × sin(angle). A missing side adjacent = hypotenuse × cos(angle).
Related guides
- Find sine, cosine and tangentGet sin, cos or tan of an angle, here sin 50, cos 50 and tan 50 in degrees.
- Find an angle from a ratioUse the inverse trig functions (sin⁻¹, cos⁻¹, tan⁻¹) to turn a ratio back into an angle.
- Use the Pythagorean theoremFind the long side (hypotenuse) of a right triangle from the two shorter sides.