Question

What are the angle measures of triangle ABC?

m∠A = 30°, m∠B = 60°, m∠C = 90°
m∠A = 90°, m∠B = 60°, m∠C = 30°
m∠A = 60°, m∠B = 90°, m∠C = 30°
m∠A = 90°, m∠B = 30°, m∠C = 60°

Answer 1

m∠A = 90°, m∠B = 60°, m∠C = 30°

Explanation:

edge2021

Answer 2

The correct option is: m∠A = 90°, m∠B = 60°, m∠C = 30°

Explanation

Given sides of the triangle are....

Opposite side of ∠A is:
`a= 24`

Opposite side of ∠B is:
`b=12√(3)` and

Opposite side of ∠C is:
`c=12`

For finding the angles of triangle ABC, we need to use the Cosine rules. So....

`cos(A)= (b^2+c^2-a^2)/(2bc)\\ \\ cos(A)=((12√(3))^2+(12)^2-(24)^2)/(2(12√(3))(12)) \\ \\ cos(A)=(432+144-576)/(288√(3))=0\\ \\ A=cos^-^1(0)=90degree\\ \\ \\ cos(B)=(a^2+c^2-b^2)/(2ac)\\ \\ cos(B)=((24)^2+(12)^2-(12√(3))^2)/(2(24)(12))\\ \\ cos(B)=(576+144-432)/(576)=(1)/(2)\\ \\ B= cos^-^1((1)/(2))=60 degree\\ \\ \\ cos(C)=(a^2+b^2-c^2)/(2ab)\\ \\ cos(C)=((24)^2+(12√(3))^2-(12)^2)/(2(24)(12√(3)))`

`cos(C)=(576+432-144)/(576√(3))=(3)/(2√(3))=(√(3))/(2)\\ \\ C=cos^-^1((√(3))/(2))=30 degree`

So, the measures of ∠A, ∠B and ∠C are 90°, 60° and 30° respectively.