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 =

Step-by-step explanation:

Right △EFG has its right angle at E, FG=12 , and EG=8

Since the right angle triangle is at E

FG = 12 is the hypotenus

EG = 8

EF =x

using pythagoras theorem

HYP²= OPPOSITE²+ ADJACENT²

FG²= EF²+EG²

12²= EF²+8²

144 = EF²+64

144-64 = EF²

80 = EF²

EF = √80 = √16X5 = √4²X5 = 4√5

csc G = ADJACENT /HYPOTENUS = EG/FG=8/12= 2/3

sin F = opposite/hypotenus = EG/FG=8/12 = 2/3

Tan F = opposite/adjacent = EG/EF= 8/4√5=2/√5

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

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.