Answer:
m∠A = 90°, m∠B = 60°, m∠C = 30°
Step-by-step explanation:
step 1
see the attached figure to better understand the problem
In this problem we have a right triangle, because the Pythagorean Theorem is satisfied
so
[tex]BC^2=AB^2+AC^2[/tex]
[tex]24^2=12^2+(12\sqrt{3}) ^2\\\\576=576[/tex]
therefore
[tex]m\angle A=90^o[/tex]
step 2
Find the measure of angle B
we know that
In the right triangle ABC
[tex]cos(B)=\frac{AB}{BC}[/tex] ----> by CAH (adjacent side divided by the hypotenuse)
substitute the given values
[tex]cos(B)=\frac{12}{24}[/tex]
[tex]m\angle B=cos^{-1}(\frac{12}{24})=60^o[/tex]
step 3
Find the measure of angle C
we know that
[tex]m\angle B+m\angle C=90^o[/tex] ----> by complementary angles
we have
[tex]m\angle B=60^o[/tex]
substitute
[tex]60^o+m\angle C=90^o\\m\angle C=30^o[/tex]
therefore
m∠A = 90°, m∠B = 60°, m∠C = 30°
