Answer:
30°
Step-by-step explanation:
You want the measure of angle A in isosceles triangle ABC with AB=BC=3 and AC=3√3.
Cosine
The altitude of the triangle divides it into two congruent right triangles, each with a hypotenuse of 3 and a long side of (3√3)/2 = 1.5√3.
The cosine of angle A is the ratio ...
Cos = Adjacent/Hypotenuse
cos(A) = AD/AB . . . . . . . where D is the midpoint of AC
cos(A) = (1.5√3)/(3) = (√3)/2
The angle is found using the inverse cosine function:
A = arccos(√3/2) = 30°
The measure of angle A is 30°.
