Trigonometry calculator
The opposite from 35° and the hypotenuse
6.88
The opposite is 6.8829…, which is 6.88 to 3 significant figures.
Working
- You know the hypotenuse and want the opposite, so use SOH: sin θ = opposite ÷ hypotenuse.
- sin 35° = x ÷ 12.
- x = 12 × sin 35° = 12 × 0.5736… = 6.88 (3 s.f.).
Your result
6.88. The opposite is 6.8829…, which is 6.88 to 3 significant figures.
Trigonometry, step by step
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Your mock plan, in three taps
In right-angled trigonometry with SOH CAH TOA, an angle of 35° and a hypotenuse of 12 cm give an opposite side of 12 × sin 35° = 6.88 cm (3 s.f.).
Questions people ask
How do you know whether to use sin, cos or tan?
Label the sides from the angle, then look at the two sides in the question (the one you know and the one you want). Opposite and hypotenuse: sin. Adjacent and hypotenuse: cos. Opposite and adjacent: tan.
How do you find an angle?
Divide the two sides in the right order for the ratio, then use the inverse button. Opposite 5 and adjacent 8: tan θ = 0.625, θ = tan⁻¹(0.625) = 32.0°.
When do you multiply and when do you divide?
If the side you want is on top of the ratio (opposite in sin), multiply. If it is underneath (hypotenuse in sin or cos, adjacent in tan), divide.
Why is my calculator giving the wrong answer?
Check it is in degrees: a D should show on the screen. In radians, sin 30 gives −0.988 instead of 0.5.
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How we work this out
What it does
Find a missing side or angle in a right-angled triangle with sin, cos and tan, and see which ratio to use and why.
Right-angled triangles: an angle between 0° and 90° and a side, or two sides.
Method
- Name the sides from the angle: opposite, adjacent and hypotenuse.
- Pick the ratio with the two sides involved: SOH, CAH or TOA.
- For a side, multiply or divide by the ratio; for an angle, use the inverse (sin⁻¹, cos⁻¹, tan⁻¹).