MHB Finding the measure of Triangle ABC

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To solve Triangle ABC with angle A at 46 degrees and side b measuring 8, start by recognizing that the sum of angles in a triangle equals 180 degrees. Since it's a right triangle, angle B can be calculated as 44 degrees. With one angle and a side known, the Law of Sines can be applied to find the lengths of sides a and c, resulting in values of approximately 8.28 and 11.52, respectively. The area of the triangle can then be determined using the Pythagorean theorem, yielding an area of about 33.14 square units. Understanding these relationships and formulas is essential for solving the triangle correctly.
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A = 46 degrees

b = 8

I don't even know how to start this and I'm really confused. I've already labeled A and b but I really have no clue on how to continue. .-. Can someone please explain this very carefully to me and use simple terms?

I've been trying to do this problem and I was told that I start it by doing 10 x sin 18, but I'm not really sure why that is done. So far I got a =0.053, I'm not sure if that's right or wrong so yeah. .-. I need to find a, b and c and I'm confused on what to multiply.
 
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What relationship must hold between $\angle A$ and $\angle B$?
 
MarkFL said:
What relationship must hold between $\angle A$ and $\angle B$?

The directions say " Solve Triangle ABC using the diagram and the given measurements. "

It's referring to the lowercase b, which is a side of the triangle in the example diagram.
 
Mizu said:
The directions say " Solve Triangle ABC using the diagram and the given measurements. "

It's referring to the lowercase b, which is a side of the triangle in the example diagram.

I am assuming you are to find the measure of all angles and sides. Since it is a right triangle, and you know the measure of one of the acute angles, what must the measure of the other be?

Once you know all 3 angles, and you know at least 1 side's measure, you can then use the Law of Sines to find the measures of the unknown sides.
 
Angles sum = 180º
B = 180º - 90º - A = 44º
Use sine law for a and c.
a = 8.28 and c = 11.52
Use Pythagoraem's theoreme for area.
area = 33.14 ( ² )
 

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