Solving Right Triangles with 3 Angles and Area - Warren

  • Context: High School 
  • Thread starter Thread starter Whalstib
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around the possibility of solving a right triangle given three angles and the area. Participants explore the implications of this scenario, particularly in relation to trigonometric principles and applications in geometry.

Discussion Character

  • Exploratory, Technical explanation, Mathematical reasoning

Main Points Raised

  • Warren questions whether it is possible to solve a right triangle with three angles (90-72-18) and a specified area (A=150).
  • One participant suggests using the Law of Sines to establish relationships between the sides, indicating that this would yield the sides up to a constant, which could then be determined using the area formula involving two sides and their included angle.
  • Warren expresses uncertainty about applying the Law of Sines, noting previous experience with SAS problems and seeking further elaboration.
  • A later reply proposes using the area formula \( A_{triangle} = \frac{1}{2}ab \sin(\gamma) \) to derive necessary information for solving the triangle.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the method for solving the triangle, and multiple approaches are discussed without resolution.

Contextual Notes

The discussion does not clarify the assumptions regarding the relationships between angles and sides, nor does it resolve the mathematical steps necessary to apply the proposed methods.

Who May Find This Useful

Individuals interested in trigonometry, geometry, and the properties of triangles may find the discussion relevant.

Whalstib
Messages
119
Reaction score
0
But I'm not getting it.

Is it possible to solve a right triangle give 3 angles and the area?

For instance 90-72-18, A=150.

What I'm trying to solve is a problem of squares to rectangles and vis versa using trigonometry. I'll use this to determine extension and contraction.

Thanks,

Warren
 
Mathematics news on Phys.org
Law of Sines will give you the relation between the sides, hence the sides up to a constant. Use the formula for area using two sides and their internal angle to determine this constant.
 
I was going in that direction but have only used this to solve SAS etc problems.

So far I have a/.31=b/.95=c/1


Could you elaborate please..

thanks,

Warren
 
Oh I got it!

Thanks!

Warren
 
Using [tex]A_{triangle} = \frac{1}{2}ab \sin(\gamma)[/tex], where a and b are sides of the triangle, and gamma is the angle between them should give you enough information to solve the triangle.

Edit: too late...
 

Similar threads

  • · Replies 38 ·
2
Replies
38
Views
6K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 10 ·
Replies
10
Views
3K
Replies
1
Views
2K
  • · Replies 17 ·
Replies
17
Views
11K
  • · Replies 9 ·
Replies
9
Views
4K