If a: B = 2:3, B: C = 1:2, and a + B + C = 66, then a=______ ．

If a: B = 2:3, B: C = 1:2, and a + B + C = 66, then a=______ ．

a: B = 2:3, B: C = 1:2 = (1 × 3): (2 × 3) = 3:6, a: B: C = 2:3:6, 66 × 22 + 3 + 6 = 12

In the triangle ABC, B = 1, C = radical 3, angle c = 2 / 3 π, then a = solution steps

Cosine theorem
c²=a²+b²-2abcos(2π/3)
3=a²+1+2×1×a×1/2
a²+a-2=0
(a+2)(a-1)=0
A = 1 or - 2 (rounding off)
a=1

Given that: a of B = 5 of 3, find: (1) the value of a + B of B, (2) the value of A-B of B

(a+b)/b=a/b+1
Just substitute a / b,
(2) In the same way

Given two points a (1, - 1), B (3,3), and point C (5, a) on the straight line AB, find the value of real number a

Let YAB = KX + B
∵A(1,-1)、 B(3,3)
∴{-1=k+b
3=3k+b
The solution is {k = 2
b=-3
∴yAB=2x-3
∵ point C (5, a) is on line ab
Let x = 5, then y = 7
∴a=7