The sin A is equal to 12/13 and the tan (A) is equal to 12/5.
RIGHT TRIANGLE
A triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.
The Pythagorean Theorem says: [tex]hypotenuse^2=(leg_1)^2+(leg_2)^2[/tex]. And the main trigonometric ratios are:
[tex]sin(\beta )= \frac{opposite\;leg}{hypotenuse} \\ \\ cos(\beta )= \frac{adjacent\;leg}{hypotenuse} \\ \\ tan(\beta )= \frac{opposite\;leg}{adjacent\;leg} \\ \\[/tex]
The question gives cos (A)=5/13. If cos (A) is represented by the quotient between the adjacent leg and the hypotenuse, you have:
adjacent leg=5
hypotenuse=13
Therefore, you can find the opposite leg of A from Pythagorean Theorem, see below.
[tex]hypotenuse^2=(leg_1)^2+(leg_2)^2\\ \\ 13^2=5^2+(leg_2)^2\\ \\ 169=25+(leg_2)^2\\ \\ 144=(leg_2)^2\\ \\ leg_2=12[/tex]
Thus, the opposite leg is equal to 12. Now, you can find sin (A) since:
[tex]sin(A)= \frac{opposite\;leg}{hypotenuse}=\frac{12}{13}[/tex]
Finally, you can find the tan (A) since:
[tex]tan(a )= \frac{opposite\;leg}{adjacent\;leg}=\frac{12}{5}[/tex]
Learn more about trigonometric ratios here:
brainly.com/question/11967894
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