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In ΔXYZ, x = 19.2 meters, y = 21 meters, and z = 19.1 meters. Find the remaining measurements of the triangle, and round your answers to the nearest tenth.
∠X = 57°, ∠Y = 66.5°, ∠Z = 56.5°
∠X = 28.6°, ∠Y = 91.2°, ∠Z = 56.5°
∠X = 28.6°, ∠Y = 91.2°, ∠Z = 60.2°
∠X = 57°, ∠Y = 66.5°, ∠Z = 60.2°

Respuesta :

calculista

Answer:

∠X = 57°, ∠Y = 66.5°, ∠Z = 56.5°

Step-by-step explanation:

step 1

Find the measure of angle X

Applying the law of cosines

[tex]x^2=y^2+z^2-2(y)(z)cos(X)[/tex]

substitute the given values

[tex]19.2^2=21^2+19.1^2-2(21)(19.1)cos(X)[/tex]

[tex]368.64=805.81-802.2cos(X)[/tex]

[tex]802.2cos(X)=805.81-368.64[/tex]

[tex]cos(X)=0.5450\\X=57.0^o[/tex]

step 2

Find the measure of angle Y

Applying the law of cosines

[tex]y^2=x^2+z^2-2(x)(z)cos(Y)[/tex]

substitute the given values

[tex]21^2=19.2^2+19.1^2-2(19.2)(19.1)cos(Y)[/tex]

[tex]441=733.45-733.44cos(Y)[/tex]

[tex]733.44cos(Y)=733.45-441[/tex]

[tex]cos(Y)=0.3987\\Y=66.5^o[/tex]

step 3

Find the measure of angle Z

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

[tex]X+Y+Z=180^o[/tex]

substitute the given values

[tex]57.0^o+66.5^o+Z=180^o[/tex]

solve for Z

[tex]Z=180^o-123.5^o=56.5^o[/tex]

Answer:

Triangle A. ∠X = 57°, ∠Y = 66.5°, ∠Z = 56.5°

Step-by-step explanation:

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