Sine: in a Right Triangle
How to find sine in a right triangle (trigonometry): formula, 3 examples, and their solutions.
Formula
Sine is the ratio of
[Opposite side]/[Hypotenuse]
in a right triangle.
The opposite side means
the side opposite to ∠A.
To remember the ratio,
remember SOH:
Sine, Opposite side, and Hypotenuse.
Example
Sine is SOH:
Sine, Opposite side, and Hypotenuse.
The Opposite side is 3.
The Hypotenuse is 5.
So,
S, sin A
is equal to,
O: opposite side, 3
over,
H: hypotenuse, 5.
So sin A = 3/5.
Example
Sine is SOH:
Sine, Opposite side, and Hypotenuse.
The Opposite side is 12.
The Hypotenuse is 13.
So,
S, sin A
is equal to,
O: opposite side, 12
over,
H: hypotenuse, 13.
So sin A = 12/13.
Example
First, find sin A
from the given right triangle.
Sine is SOH:
Sine, Opposite side, and Hypotenuse.
The Opposite side is x.
The Hypotenuse is 10.
So,
S, sin A
is equal to,
O: opposite side, x
over,
H: hypotenuse, 10.
Next, it says
sin A = 4/5.
So write
[ = 4/5].
So sin A = x/10 = 4/5.
Solve x/10 = 4/5.
Multiply 10 to both sides.
Then x = [4/5]⋅10.
Cancel the denominator 5
and reduce the numerator 10 to, 10/5, 2.
4⋅2 = 8
So x = 8.