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Trigonometry in a right triangle

In a right triangle, sine, cosine and tangent relate the angle vv to the ratio between the sides. The Pythagorean theorem relates the sides without any angles.

sin⁡v=oppositehypotenuse, cos⁡v=adjacenthypotenuse\sin v = \frac{\text{opposite}}{\text{hypotenuse}},\ \cos v = \frac{\text{adjacent}}{\text{hypotenuse}}sine and cosine
a2+b2=c2a^2 + b^2 = c^2the Pythagorean theorem, cc is the hypotenuse

Symbols

vvacute angle°
cchypotenuse (longest side)

Example

A ramp is 4.0 m long and rises 0.80 m: sin⁡v=0.804.0=0.20⇒v≈11.5∘\sin v = \frac{0.80}{4.0}=0.20 \Rightarrow v\approx 11.5^\circ, and the ground length is 4.02−0.802≈3.92\sqrt{4.0^2-0.80^2}\approx 3.92 m.

Check that the calculator is in DEG mode when the angle is in degrees, otherwise the answer is completely wrong.
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Part of Foundations of Mathematics: Trigonometry and geometry.