Question

In triangle ABC ,AB=12cm,angle A =45°and angle B=30°,Find the area of triangle ABC,Find the ratio of the sides of the triangle having angles 30° ,40° and 105°

Answer 1

Step-by-step explanation:

In the triangle above the angle A = 105 degrees, angle B = 30 degrees and the length of the side Ac= 8. How can I find the length of the side AB?

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Well, I have recently learnt about “Sine Theorem”, “Cosine Theorem” and “Tangent Theorem”, so I will try my best to answer this question!

Here we go, get a look at the picture which I have drawn-

So, let’s get started-

In the question, angle A= 105°,

Then, angle B= 30°

So, angle C= 45° (obviously)

And, AC= 8 unit (as you have not provided any specific unit)

So, applying the so called, “Sine Theorem” over here-

sin B/AC = sin C/AB

So, sin 30°/8 = sin 45°/AB

Let’s get this quick-

Putting the value of sin 30° and sin 45°,

AB= 8*{(2)^(1/2)} unit

So, AB= 8*1.414 unit

Thus, we arrived at our final result-

AB= 11.312 unit (approximately)

Thanks!;).