Respuesta :

altavistard

Answer:

the sine of the angle Ф is opp / hyp, or √57/11

Step-by-step explanation:

Find sin Ф where Ф is the angle shown.

Since the sine function is defined as the value of the ratio

opp side / hypotenuse, we must find the length of the opp side.  Using the Pythagorean Theorem, we get:

11² = opp² + 8², which leads to opp² = 121 - 64, so that opp = √57.

Then the sine of the angle Ф is opp / hyp, or √57/11

[tex]\frac{\sqrt{57}}{11}[/tex]

Sine is the trigonometric function that for an acute angle is the ratio between the leg opposite the angle when it is considered part of a right triangle and the hypotenuse. Cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse.

Consider the given figure.

[tex]\cos \theta=\frac{8}{11}[/tex]

[tex]\sin \theta=\sqrt{1-\cos^2\theta}[/tex]

       [tex]=\sqrt{1-\left ( \frac{8}{11} \right )^2}[/tex]

       [tex]=\sqrt{1-\frac{64}{121}}[/tex]

       [tex]=\sqrt{\frac{57}{121}}[/tex]

       [tex]=\frac{\sqrt{57}}{11}[/tex]

For more information:

https://brainly.com/question/3827723?referrer=searchResults

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