Answer:
HI: 17.9
GH: 22.1
Step-by-step explanation:
1) There are three trigonometric ratios for right-angled triangles.
Sin = opposite/hypotenuse
Cos = adjacent/hypotenuse
Tan = opposite/adjacent.
2) Opposite to the 90° lies the hypotenuse. Opposite to the given angle lies the opposite.
Beside the given angle lies the adjacent.
3) The value of G given to us is 54°. The length of GI is 13. We are asked to find the lengths of HI and GH. We cannot find GH (we can, but I prefer the current method) without the length of HI. Let's find HI.
Tan(54) = x/13
Tan(54) × 13 = x
x = 17.89
4) We can use the Pythagorean theorem to find the length of GH. His theorem is c² = a² + b².
c² = a² + b²
c² = 13² + 17.89²
c² = 489.0521
c = √489.0521
c = 22.11
5) Round off the answers to the nearest tenth.
HI = 17.9
GH = 22.1
