A right triangle has side lengths 3, 4, and 5 as shown below. [tex]\sin(A) = \dfrac{\text{3}}{\text{5}}[/tex][tex]\cos(A) = \dfrac{\text{4}}{\text{5}}[/tex][tex]\tan(A) = \dfrac{\text{3}}{\text{4}}[/tex].
What are the trigonometric ratios?
Trigonometric ratios for a right-angled triangle are from the perspective of a particular non-right angle.
Given;
For angle A
Base = 4
Perpendicular = 3
Hypotenuse = 5
We know that
[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}[/tex]
So, the functions are
[tex]\sin(A) = \dfrac{\text{3}}{\text{5}}[/tex]
[tex]\cos(A) = \dfrac{\text{4}}{\text{5}}[/tex]
[tex]\tan(A) = \dfrac{\text{3}}{\text{4}}[/tex]
Thus, A right triangle has side lengths 3, 4, and 5 as shown below. [tex]\sin(A) = \dfrac{\text{3}}{\text{5}}[/tex][tex]\cos(A) = \dfrac{\text{4}}{\text{5}}[/tex][tex]\tan(A) = \dfrac{\text{3}}{\text{4}}[/tex].
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