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?

Answer 1

Answer:

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

Answer 2

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