Question

Please help me with this.

Answer 1

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: $hypotenuse^2=(leg_1)^2+(leg_2)^2$. And the main trigonometric ratios are:

$sin(\beta )= \frac{opposite\;leg}{hypotenuse} \\ \\ cos(\beta )= \frac{adjacent\;leg}{hypotenuse} \\ \\ tan(\beta )= \frac{opposite\;leg}{adjacent\;leg}$

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.

$hypotenuse^2=(leg_1)^2+(leg_2)^2\\ \\ 13^2=5^2+(leg_2)^2\\ \\ 169=25+(leg_2)^2\\ \\ 144=(leg_2)^2\\ \\ leg_2=12$

Thus, the opposite leg is equal to 12. Now, you can find sin (A) since:

$sin(A)= \frac{opposite\;leg}{hypotenuse}=\frac{12}{13}$

Finally, you can find the tan (A) since:

$tan(a )= \frac{opposite\;leg}{adjacent\;leg}=\frac{12}{5}$

Learn more about trigonometric ratios here:

brainly.com/question/11967894

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