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Use the information given in the diagram of TriangleGHI to find the missing measurements. Round all answers to the nearest tenth.
m∠G = °
HI =
GH =

Use the information given in the diagram of TriangleGHI to find the missing measurements Round all answers to the nearest tenth mG HI GH class=

Respuesta :

Answer:

m<G = 51

HI= 23.3

GH = 18.9

Step-by-step explanation:

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  m∠G = 51°, GH = 18.9 and HI = 23.3 will be the answer.

Trigonometric properties of a right triangle:

  •  Sum of the measures of interior angles of a triangle is 180°.
  •  cosine of an angle is represented by,

          cosθ = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

  •  Sine of the angle is represented by,

          sinθ = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

Given in the question,

  •   Measure of an angle = 39°
  •   Measure of the hypotenuse = 30

Since, sum of all angles of ΔGHI = 180°,

m∠G + m∠H + m∠I = 180°

m∠G + 90° + 39° = 180°

m∠G + 129° = 180°

m∠G = 51°

By applying sine rule,

sin(39)° = [tex]\frac{GH}{30}[/tex]

GH = 30.sin(39°)

GH = 18.88 ≈ 18.9

By applying cosine rule,

cos(39°) = [tex]\frac{HI}{30}[/tex]

HI = 23.31 ≈ 23.3

       Therefore, m∠G = 51°, GH = 18.9 and HI = 23.3 will be the answer.

Learn more about the trigonometric ratios here,

https://brainly.com/question/26717376?referrer=searchResults

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