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What are the angle measures of triangle ABC?
mA= 30°, m ZB = 60°, m 2C = 90°
mZA= 90°, m ZB = 60°, m 2C = 30°
mZA= 60°, m ZB = 90°, m2C = 30°
mZA= 90°, m ZB = 30°, m2C = 60°

What are the angle measures of triangle ABC mA 30 m ZB 60 m 2C 90 mZA 90 m ZB 60 m 2C 30 mZA 60 m ZB 90 m2C 30 mZA 90 m ZB 30 m2C 60 class=

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bhuvna789456

∠A = 90°, ∠B = 60° and ∠C = 30°

Step-by-step explanation:

  • Step 1: Find whether the triangle is a right angled triangle by using Pythagoras theorem. Given sides are a = 24 (opposite to ∠A), b = 12√3 (opposite to ∠B) and c = 12 (opposite to ∠C).

⇒ 12² + (12√3)² = 144 + 432 = 576

⇒ √576 = 24 = a.  This shows that the triangle is a right angled triangle.

So ∠A = 90°

  • Step 2: Use trigonometric equations to determine the other angles.

⇒ cos B = AB/BC = 12/24 = 1/2

⇒ ∠B = 60°

  • Step 3: The sum of the angles in a triangle is 180°. To find ∠C,

⇒ ∠C = 180° - (90° + 60°) = 180° - 150°

⇒ ∠C = 30°

adioabiola

The angle measures of triangle ABC is therefore;

mZA= 90°, m ZB = 60°, m ZC = 30°

Angle measures of Right triangles

By testing for Pythagoras triple;

  • 24² = 12² + (12√3)²

  • 576 = 144 + 432

  • 576 = 576.

Hence, the triangle is a right-angled triangle.

We can then evaluate mZC as follows;

  • Sin C = 12/24 = 0.5

  • C = Sin-¹(0.5) = 30°

  • And angle B = 180 - 30 -90

  • Angle, B = 60°

Read more on angle measures in triangles;

https://brainly.com/question/11664714

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