In aδabc, if ∠b = 60° and the ratio of two sides is a : c = 2 : √3 + 1, then ∠a=

∠A= 45°

Step-by-step explanation:

To find  ∠A first we have to find the length of side B by cosine law:

b^2 = a^2 + c^2 – 2 a c cos B

b^2=(2)^2 +(√3 + 1)^2 - 2(2)(√3 + 1) cos 60

b^2 = 6

Taking square root at both sides:

√b^2 = √6

b= 2.45

Now we can calculate ∠A by sine law:

b / sin B = a / sin A

2.45 / sin 60 = 2 / sin A

sin A= 2* √3/2 /2.45

sin A = 2√3/2 * 1/2.45

sinA = 2√3/ 4.9

sin A = 0.7069

sin A = 0.707

A=45°

Thus ∠A= 45°

10 * 563.67 = 5636.7