The corrected trigonometric ratios are: tanA=4/3, sinA=4/5 and sinB=3/5.
RIGHT TRIANGLE
A triangle is classified as a right triangle when it presents one of your angles equal to 90º. The Pythagorean Theorem ([tex]hypotenuse^2=(side1)^2+(side2)^2[/tex]) is very used in this type of this triangle because from this theorem, it is possible finding angles or sides.
Another math tool applied for finding angles or sides in a right triangle is trigonometric ratios.
[tex]sin(\alpha) =\frac{opposite \; side}{hypotenuse} \\ \\ cos (\alpha) =\frac{adjacent\; side}{hypotenuse}\\ \\ tan(\alpha) = \frac{sin(\alpha )}{cos (\alpha )}= \frac{opposite \; side}{adjacent\; side}[/tex]
Given data:
C= right angle
AC=3
BC=4
If C is the right angle, the hypotenuse is represented for the side AB. For finding the hypotenuse, you should apply the Pythagorean Theorem.
[tex]hypotenuse^2=(side1)^2+(side2)^2\\ \\ AB^2=AC^2+BC^2\\ \\ AB^2=3^2+4^2\\ \\ AB^2=9+16\\ \\ AB^2=25\\ \\ AB=\sqrt{25}=5[/tex]
After that, you should find the trigonometric ratios for the angles A and B.
[tex]sin(A) =\frac{opposite \; side}{hypotenuse}=\frac{BC}{AB}=\frac{4}{5} \\ \\ cos (A) =\frac{adjacent\; side}{hypotenuse}=\frac{AC}{AB}=\frac{3}{5} \\ \\ tan(A) = \frac{sin(A)}{cos (A )} =\frac{opposite \; side}{adjacent\; side}=\frac{BC}{AC} =\frac{4}{3}[/tex]
[tex]sin(B) =\frac{opposite \; side}{hypotenuse}=\frac{AC}{AB}=\frac{3}{5} \\ \\ cos (B) =\frac{adjacent\; side}{hypotenuse}=\frac{BC}{AB}=\frac{4}{5} \\ \\ tan(B)= \frac{sin(B)}{cos (B )} =\frac{opposite \; side}{adjacent\; side}=\frac{AC}{BC} =\frac{3}{4}[/tex]
Therefore, the corrected trigonometric ratios are: tanA=4/3, sinA=4/5 and sinB=3/5
Learn more about trigonometric ratios here:
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