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how is sin a = perpendicular by base

how is sin a = perpendicular by base

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1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

First what you have written is wrong.
sina = \frac{Perpendicular}{Hypotenuse}
tana = \frac{Perpendicular}{Base}
Well there is no particular reason behind this.
You can understand in this way.
tan(a) is defined as a slope.
Lets assume a point P(x, y) in the coordinate plane.
Join this point to origin O(0, 0).
Now, slope of OP is
\frac{y}{x}
Projection of OP on x-axis is x. Lets point A (x, 0)
Now we have triangle OAP, in which
tan(a) = \frac{y}{x} = \frac{AP}{OA}
tan(a) = \frac{Perpendicular}{Base}
By Definition, we have
tan(a) = \frac{sin(a)}{cos(a)}
From here, we have
sin(a) = \frac{Perpendicular}{Hypotenuse}

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