Finding the measure of Triangle ABC

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SUMMARY

The discussion focuses on solving Triangle ABC, where angle A is 46 degrees and side b measures 8 units. To find the remaining angles and sides, the Law of Sines is applied, leading to angle B being calculated as 44 degrees. The lengths of sides a and c are determined to be 8.28 and 11.52 units, respectively, and the area of the triangle is calculated to be 33.14 square units. The relationship between the angles and the application of trigonometric laws are crucial for solving the triangle.

PREREQUISITES
  • Understanding of basic trigonometry, specifically the Law of Sines
  • Knowledge of triangle properties, including angle sum and right triangle relationships
  • Familiarity with Pythagorean theorem for area calculations
  • Ability to perform sine calculations and angle measurements
NEXT STEPS
  • Study the Law of Sines in detail for solving non-right triangles
  • Learn how to apply the Pythagorean theorem in various triangle scenarios
  • Explore angle relationships in triangles, including complementary angles
  • Practice solving different types of triangles using given measurements
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Students studying geometry, mathematics educators, and anyone looking to enhance their skills in solving triangles using trigonometric principles.

Mizu
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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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