Step-by-step explanation:
Since we are not given the required parameters, we can use the following parameters
Given:
∠
A = 5
x
+
30
°
∠
B = 2
x
Since △ABC is isosceles with AB = BC, then ∠
A = ∠
C (the base angles of an isosceles triangle are equal)
Since sum of angle in a triangle are the same, then;
∠
A + ∠
B + ∠
C = 180°
Substitute the given functions and get x;
5x+30 + 2x + 5x+30 = 180
12x + 60 = 180
12x = 180-60
12x = 120
x = 120/12
x = 10°
∠
A = 5x+30
∠
A = 5(10)+30
∠
A = 80°
Since ∠
A =∠
C
∠
C = 80°
For ∠
B;
∠
B = 2x
∠
B = 2(10)
∠
B = 20°
Let AB = 1, since AB = BC, BC = 1
To get AC, use the sin rule;
a/sin∠
A = b/sin∠
B
a/sin80 = 1/sin20
asin20 = sin80
a = sin80/sin20
a = 0.9848/0.3420
a = 2.879
Hence AC ≈ 3
Note that the values of the sides and angles are assumed.