Question

a=2, A=30°,c=60° then find side c
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Answer 1

Answer:

Question

In triangle ABC, A = 30°, B = 60°, then find a:b:c.

Solution

We are provided that :-

∠A = 30°

∠B = 60 °

Then as from angle sum property of a triangle :-

Sum of all three angles is equal to 180°

Then

∠A + ∠B + ∠C = 180°

→ 30° + 60° + ∠C = 180°

→ 90° + ∠C = 180°

→ ∠C = 180° - 90°

→ ∠C = 90°

Now as it is asked to find out the ratio of a : b : c

a = side opposite of 30° (∠A)

b = side opposite of 60° (∠B)

c = side opposite of 90° (∠C)

Now as one of the angle is 90° hence ∆ABC is a right angle Triangle

Now as we know that in right angle Triangle :-

Side in front of θ /Hypotenuse = sinθ

Then

sin 60° = √3/2

sin 30° = 1/2

Now in our triangle :-

sin 60° = b/c

sin 30° = a/c

then a : b = 1 : √3

Also

a : c = 1 : 2

b : c = √3 : 2

So

a : b : c

= 1 : √3 : 2$\huge$

Answer 2

Answer:

We are provided that :-

∠A = 30°

∠B = 60 °

Then as from angle sum property of a triangle :-

Sum of all three angles is equal to 180°

Then

∠A + ∠B + ∠C = 180°

→ 30° + 60° + ∠C = 180°

→ 90° + ∠C = 180°

→ ∠C = 180° - 90°

→ ∠C = 90°

Now as it is asked to find out the ratio of a : b : c

a = side opposite of 30° (∠A)

b = side opposite of 60° (∠B)

c = side opposite of 90° (∠C)

Now as one of the angle is 90° hence ∆ABC is a right angle Triangle

Now as we know that in right angle Triangle :-

Side in front of θ /Hypotenuse = sinθ

Then

sin 60° = √3/2

sin 30° = 1/2

Now in our triangle :-

sin 60° = b/c

sin 30° = a/c

then a : b = 1 : √3

Also

a : c = 1 : 2

b : c = √3 : 2

So

a : b : c

= 1 : √3 : 2