Finding the measure of Triangle ABC

In summary, to solve Triangle ABC using the given measurements, you need to find the measure of all angles and sides. Since it is a right triangle, one of the acute angles must be 44º. Then, using the Law of Sines, you can find the measures of the unknown sides, which are a = 8.28 and c = 11.52. Finally, use Pythagorean's theorem to find the area of the triangle, which is 33.14 (²).
  • #1
Mizu
2
0
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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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  • #2
What relationship must hold between $\angle A$ and $\angle B$?
 
  • #3
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.
 
  • #4
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.
 
  • #5
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 )
 

FAQ: Finding the measure of Triangle ABC

What is the formula for finding the measure of a triangle?

The formula for finding the measure of a triangle is A = ½bh, where A represents the area, b represents the base, and h represents the height.

How do I find the measure of the base of a triangle?

The base of a triangle can be found by measuring the distance between any two vertices of the triangle.

Can I use the same formula to find the measure of any type of triangle?

Yes, the formula for finding the measure of a triangle can be used for any type of triangle, including equilateral, isosceles, and scalene triangles.

Is there a difference between finding the measure of a right triangle and a non-right triangle?

Yes, the formula for finding the measure of a right triangle is slightly different and involves using the Pythagorean theorem (a² + b² = c²) to find the missing side length.

How do I know which side is the base of a triangle?

The base of a triangle is typically denoted by the lowercase letter 'b' and is usually the side that is perpendicular to the height of the triangle.

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