By knowing the length of the three sides of the triangle and applying the law of the cosine, we find that the measure of the three angles are 33.544°, 114.998° and 31.458°.
How to find the missing angles of a triangle
In this question we know the length of the three sides of a triangle, we can find the measure of all angles by using the law of the cosine. So, we know that:
a = 270, b = 442.85, c = 255
Then, by the law of the cosine:
[tex]\cos A = \frac{270^{2}-255^{2}-442.85^{2}}{-2\cdot (442.85)\cdot (255)}[/tex]
A ≈ 33.544°
[tex]\cos B = \frac{442.85^{2}-270^{2}-255^{2}}{-2\cdot (270)\cdot (255)}[/tex]
B ≈ 114.998°
[tex]\cos C = \frac{255^{2}-270^{2}-442.85^{2}}{-2\cdot (270)\cdot (442.85)}[/tex]
C ≈ 31.458°
By knowing the length of the three sides of the triangle and applying the law of the cosine, we find that the measure of the three angles are 33.544°, 114.998° and 31.458°.
To learn more on law of cosine: https://brainly.com/question/13098194
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