Question

Right △EFG has its right angle at E, FG=12 , and EG=8. What is the value of the trigonometric ratio of an angle of the triangle?

csc G =
sin F =
tan F =

Answer 1

Answer:

Step-by-step explanation:

The diagram of the right angle triangle is shown in the attached photo. To determine EF, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

12² = 8² + EF²

144 = 64 + EF²

EF² = 144 - 64 = 80

EF = √80 = 8.94

1) To determine Sin G, we would apply the Sine trigonometric ratio which is expressed as

Sin θ = opposite side/hypotenuse. Therefore,

Sin G = 8.94/12

CSC G = 1/Sin G = 12/8.94

2) taking F as the reference angle,

EG = opposite side

FG = hypotenuse

SinF = 8/12

3) Tan F = opposite side/adjacent side

Tan F = 8/8.94

Answer 2

The trigonometric ratio ae following:

                 $cosec(G)=\frac{GF}{EF}=\frac{12}{4\sqrt{5} }=\frac{3\sqrt{5} }{5}\\ \\ sin(F)=\frac{EG}{FG}=\frac{8}{12}=\frac{2}{3}\\ \\ tan(F)=\frac{EG}{EF}=\frac{8}{4\sqrt{5} } =\frac{2\sqrt{5} }{5}$

Right angle triangle:

Given that, right angle △EFG  , in which E is right angle.

            $FG=12$  and $EG=8$

Apply Pythagoras theorem,

        $EF^{2}=(12)^{2}-8^{2} \\\\EF^{2}=144-64=80\\\\EF=\sqrt{80}=4\sqrt{5}$

Triangle EFG is attached below,

The trigonometric ratio of an angle of the triangle are shown below,

        $cosec(G)=\frac{GF}{EF}=\frac{12}{4\sqrt{5} }=\frac{3\sqrt{5} }{5}\\ \\ sin(F)=\frac{EG}{FG}=\frac{8}{12}=\frac{2}{3}\\ \\ tan(F)=\frac{EG}{EF}=\frac{8}{4\sqrt{5} } =\frac{2\sqrt{5} }{5}$

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