Let triangle ABC have lengths of sides opposite angles A and C as 2 and 6 units, respectively. If angle C is 60°, then find angle A.
Answer (1)
To find angle A in triangle ABC, where side opposite angle A is 2 units, side opposite angle C is 6 units, and angle C is 60°, we can use the Law of Sines.
The Law of Sines states:
sin A a = sin B b = sin C c
In this case, we have:
a = 2 (opposite angle A)
c = 6 (opposite angle C)
C = 6 0 ∘ (angle C)
We want to find angle A.
First, let's apply the Law of Sines to find sin A :
sin A 2 = sin 6 0 ∘ 6
Since sin 6 0 ∘ = 2 3 , substitute this in:
sin A 2 = 2 3 6
Simplify the right side:
sin A 2 = 3 6 × 2 = 3 12
Now, to find sin A , solve for it by rearranging:
sin A = 12 2 × 3
Simplify:
sin A = 6 3
Now, determine angle A using the arcsine function:
\A = sin − 1 ( 6 3 )
Using a calculator, sin − 1 ( 6 3 ) approximately equals 16.26°. Therefore, angle A is approximately 16.26°.
