Question

For Exercises 1-3, find sin A, cos A, and tan A.

2.
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Answer 1

From the values of the trigonometric table, you will find: sin (A)=$\frac{\sqrt{2} }{2}$, cos(A)=$\frac{\sqrt{2} }{2}$ and tan (A)=1.

Trigonometric Ratios

The main trigonometric ratios for a right triangle are presented below.

              $sin(x)=\frac{opposite\;side}{hypotenuse} \\ \\ cos(x)=\frac{adjacent\;side}{hypotenuse}\\ \\ tan (x)= \frac{sin(x)}{cos(x)} =\frac{opposite\;side}{hypotenuse}*\frac{hypotenuse}{adjacent\;side}=\frac{opposite\;side}{adjacent\;side}$

Trigonometric Table

Angle      SinΘ      CosΘ      TanΘ

30°             $\frac{1}{2}$               $\frac{\sqrt{3} }{2}$              $\frac{\sqrt{3} }{3}$

45°             $\frac{\sqrt{2} }{2}$            $\frac{\sqrt{2} }{2}$              $1$

60°             $\frac{\sqrt{3} }{2}$               $\frac{1}{2}$           ${\sqrt{3} }$

For solving this question, you need to apply the a trigonometric ratio . You have the dimensions of one side and the values for two angles: 45° and 90°.

Knowing that the sum of angles of a triangle is equal to 180°, you can find angle A.

A+45+90=180

A=180+135

A=45°

For A=45°, from the trigonometric table, you will have:

$sin(A)=\frac{\sqrt{2} }{2} \\ \\ cos (A)=\frac{\sqrt{2} }{2}\\ \\ tan(A)=1$

Learn more about trigonometric ratios here:

brainly.com/question/11967894