Question

NEED HELP DUE FRIDAY!!!!!!!!!

If the coordinates of point I are (9, 12), what is the value of cos(G), sin(G), and tan(G) for triangle GHI? Explain your reasoning.

Answer 1

Explanation:

remember the triangle in a circle, when you learned about sine, cosine and the other trigonometric functions ?

this looked the same way, just that the circle was the norm-circle with radius 1.

here, now, the radius is larger, so every function line is also multiplied by the actual radius.

but the principles are the same.

sine is the up/down leg of the right-angled triangle.

cosine is the left/right leg.

tangent is sine/cosine.

I = (9, 12)

so, Pythagoras gives us the radius (line GI) :

GI² = GH² + HI² = 9² + 12² = 81 + 144 = 225

GI = sqrt(225) = 15

sin(G) × GI = HI

sin(G) × 15 = 12

sin(G) = 12/15 = 4/5 = 0.8

cos(G) × GI = GH

cos(G) × 15 = 9

cos(G) = 9/15 = 3/5 = 0.6

tan(G) = sin(G)/cos(G) = 4/5 / 3/5 = (4×5)/(5×3) =

= 4/3 = 1.333333333...

Answer 2

cos G = 3/5

sin G = 4/5

tan G = 4/3

Explanation:

I(9, 12)

GH = 9

HI = 12

(GI)² = 9² + 12²

GI = 15

For <G:

opp = HI = 12

adj = GH = 9

hyp = GI = 15

cos G = adj/hyp = 9/15 = 3/5

sin G = opp/hyp = 12/15 = 4/5

tan G = opp/adj = 12/9 = 4/3