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In ΔEFG, the measure of ∠G=90°, EG = 11, FE = 61, and GF = 60. What ratio represents the sine of ∠F?

Sagot :

Answer:

sinF = [tex]\frac{11}{61}[/tex]

Step-by-step explanation:

sinF = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{EG}{FE}[/tex] = [tex]\frac{11}{61}[/tex]

The ratio which represents the sine of ∠F is [tex]\frac{11}{61}[/tex].

What is sine of an angle?

In a right angled triangle, the sine of an angle is the length of the side opposite the angle divided by the length of the hypotenuse.

Formula for sine of an angle

sin θ = opposite side w.r.t θ / hypotenuse

According to the given question

We have

A right angle triangle EFG, in which

∠G = 90 degree

EG = 11

FE = 61

and,  GF = 60

Now, the opposite side with respect to ∠F is GE

and the hypotenuse is EF

Therefore, sine of ∠F = side which is opposite w.r.t ∠F/ hypotenuse

⇒ [tex]sinF=\frac{GE}{EF}[/tex]

⇒ [tex]SinF=\frac{11}{61}[/tex]

Hence, the ratio which represents the sine of ∠F is [tex]\frac{11}{61}[/tex].

Learn more about sine of an angle here:

https://brainly.com/question/13656175

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