Right-Triangle Trigonometry
SOH-CAH-TOA relates the angles to the sides.
The rules
- sin = opposite / hypotenuse, cos = adjacent / hypotenuse, tan = opposite / adjacent.
- Label the sides relative to the angle you are using.
- Use inverse trig (sin⁻¹, etc.) to find an angle.
- Check that your calculator is in degree mode.
Watch out: Using the wrong side as 'opposite.'
Worked example
A 12-foot ladder makes a 60° angle with the ground. How high does it reach?
- Height is opposite the 60° angle.
- sin 60° = h/12, so h = 12 · (√3/2) = 6√3.
Answer: 6√3 ft
Try it yourself
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