Tangent: in a Right Triangle
How to find sine in a right triangle (trigonometry): formula, meaning, 3 examples, and their solutions.
Formula
Tangent is the ratio of
[Opposite side]/[Adjacent]
in a right triangle.
The opposite side means
the side opposite to ∠A.
The adjacent side means
the side adjancent to ∠A
(which is not the hypotenuse).
To remember the ratio,
remember TOA:
Tangent, Opposite side, and Adjacent side.
Meaning
tan A
= [Opposite side]/[Adjacent side]
= [change of y]/[change of x]
The slope of a line is
m
= [y2 - y1]/[x2 - x1]
= [change of y]/[change of x].
So tangent means
the slope of a right triangle.
Example
Tangent is TOA:
Tangent, Opposite side, and Adjacent side.
The Opposite side is 3.
The Adjacent side is 4.
So,
T, tan A
is equal to,
O: opposite side, 3
over,
A: adjacent side, 4.
So tan A = 3/4.
Example
Tangent is TOA:
Tangent, Opposite side, and Adjacent side.
The Opposite side is 12.
The Adjacent side is 5.
So,
T, tan A
is equal to,
O: opposite side, 12
over,
A: adjacent side, 5.
So tan A = 12/5.
Example
First, find tan A
from the given right triangle.
Tangent is TOA:
Tangent, Opposite side, and Adjacent side.
The Opposite side is x.
The Adjacent side is 12.
So,
T, tan A
is equal to,
O: opposite side, x
over,
A: adjacent side, 12.
Next, it says
tan A = 7/6.
So write
[ = 7/6].
So tan A = x/12 = 7/6.
Solve x/12 = 7/6.
Multiply 12 to both sides.
Then x = [7/6]⋅12.
Cancel the denominator 6
and reduce the numerator 12 to, 12/6, 2.
7⋅2 = 14
So x = 14.