The given triangle has three angles with measurements: ∠A = 69°, ∠B = 52°, and ∠C = 59° respectively. Using the law of cosines, these angles are calculated from the given lengths of the triangle.
<h3>What is the law of cosines?</h3>
The law of cosines gives the relationship between the lengths of sides and the angles of the triangle ABC.
According to the law of cosines:
Cos A = (b² + c² - a²)/2bc
Cos B = (a² + c² - b²)/2ac
Cos C = (a² + b² - c²)/2ab
<h3>Calculation:</h3>
For the given triangle ABC,
a = 75, b = 63, and c = 69
So, using the law of cosines,
Cos A = (b² + c² - a²)/2bc
⇒ Cos A = (63² + 69² - 75²)/2×63×69
⇒ Cos A = 5/14
⇒ A = Cos⁻¹(5/14) = 69.07
∴ ∠A = 69°
Similarly,
Cos B = (a² + c² - b²)/2ac
⇒ Cos B = (75² + 69² - 63²)/2×75×69
⇒ Cos B = 31/50
⇒ B = Cos⁻¹(31/50) = 51.6 ≅ 52
∴ ∠B = 52°
Cos C = (a² + b² - c²)/2ab
⇒ Cos C = (75² + 63² - 69²)/2×75×63
⇒ Cos C = 179/350
⇒ C = Cos⁻¹(179/350) = 59.2
∴ C = 59°
Thus, the angles of the triangle ABC are 69°, 52°, and 59° respectively.
Learn more about the law of cosines here:
brainly.com/question/8288607
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