Question

Consider a triangle ABC

Answer 1

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.

What is the law of cosines?

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

Calculation:

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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