NEED HELP Finding the length of an angle on a right triangle

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Homework Help Overview

The problem involves finding the measurement of an angle in a right triangle, where the lengths of the sides are provided: 18,944 for one leg, 30,556 for the other leg, and 35,952 for the hypotenuse. The right angle is between the two legs, and the focus is on determining the angle between the hypotenuse and one of the legs.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss using trigonometric functions such as sine, cosine, and tangent to find the angle. There is an attempt to clarify which ratios to use based on the triangle's configuration. Some participants suggest using the law of cosines as an alternative method.

Discussion Status

The discussion has explored various approaches to finding the angle, including the use of trigonometric ratios and the law of cosines. Some participants have provided guidance on setting up the equations, while others have questioned the efficiency of certain methods. There is no explicit consensus on a single approach, but multiple lines of reasoning are being examined.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. The original poster expresses uncertainty about which numbers to use in their calculations.

dominus96
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Homework Statement



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l../
l./
l/

^This is a right triangle (not drawn to scale). The left side is 18,944, then top side is 30,556, and the hypotenuse is 35,952. The right angel is between the left side and the top side. Now, how do I find the measurement of the angle between the hypotenuse and the left side?

Homework Equations



sin, cos, and tan?

The Attempt at a Solution



Since the angle is between the hypotenuse and the adjacent, I assume that I do cos, but I don't know what numbers to use.
 
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For the angle from vertical (left side) and hypotenuse, 18,944 = 35,952 cos [itex]\theta[/itex].
 
there's a relationship between the size of a leg and the vertex angle (the angle opposite of the leg)
 
You can use any of them to find the angle since you know all three lengths, you just have to setup the right ratios.
 
dominus96 said:
sin, cos, and tan?



Since the angle is between the hypotenuse and the adjacent, I assume that I do cos, but I don't know what numbers to use.

You can use any of the trig functions that you have listed to establish the proper relationship. But, for now we can stick to cos.

What ratio does cos represent? [tex]\cos\theta=\frac{?}{?}[/tex]

Casey
 
cos of angle = adjacent/hypotenuse

So, cos x = 18,944/35,952 right?
 
Use the law of cosine: http://en.wikipedia.org/wiki/Law_of_cosines

Let A = 18944, B = 30556, C = 35952

B^2 = A^2 + C^2 - 2*A*C*cos(angleB)
cos(angleB) = (A^2 + C^2 - B^2 ) / (-2*A*C)

Solve using inverse cosine, and you get B.
 
Last edited:
Thank you guys I got it.
 
Kster said:
Use the law of cosine: http://en.wikipedia.org/wiki/Law_of_cosines

Let A = 18944, B = 30556, C = 35952

B^2 = A^2 + C^2 - 2*A*C*cos(angleB)
cos(angleB) = (A^2 + C^2 - B^2 ) / (-2*A*C)

Solve using inverse cosine, and you get B.

Why? I mean you can but it's a complete waste of time in this situation :-/
 

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