The value of sin A is equal to [tex]\frac{5}{13}.[/tex]
RIGHT TRIANGLE
A triangle is classified as a right triangle when it presents one of your angles equal to 90º. In this triangle from the trigonometric ratios or the Pythagoras Theorem ([tex]hypotenuse^2=(side_1)^2+(side_2)^2[/tex]), it is possible finding angles or sides.
Trigonometric Ratios
The main trigonometric ratios for a right triangle are presented below.
[tex]sin\alpha =\frac{opposite \; side}{hypotenuse}[/tex]
[tex]cos\alpha =sin\alpha =\frac{adjacent\; side}{hypotenuse}[/tex]
[tex]tan\alpha =\frac{opposite \; side}{adjacent\; side}[/tex]
The question asks the sin A. First, you should find the hypotenuse from Pythagoras Theorem.
[tex]hypotenuse^2=(10)^2+(24)^2\\ \\ hypotenuse^2=100+576\\\\ hypotenuse^2=676\\ \\ hypotenuse=26[/tex]
Now you can find sin A.
[tex]sin\A=\frac{10}{26}=\frac{5}{13}[/tex]
Learn more about trigonometric ratios here:
brainly.com/question/11967894
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