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**Neha****Member**- Registered: 2006-10-11
- Posts: 173

solve the triangle below for its unkown parts:

ok the unkown parts are the top of the triangle which is B degrees

the left side point of the triangle is 65 degrees

right side point is C degrees

and

one side of the triangle the left side is 11inches

the other side of the triangle the right side is A inches

teh bottom of the triangle is 15inches

now i did:

65dg + C + B = 180

65dg + 65dg + B = 180

( i wrote 65dg for C angle because both sides have to be equal in my view. )

anyways

130 + B = 180

180 - 130 = 50

B = 50

C = 65

and now we have to find A side.

do like this :

11^2 + A^2 = 15^2

no right?

*Last edited by Neha (2006-12-04 07:38:28)*

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**pi man****Member**- Registered: 2006-07-06
- Posts: 251

You made a couple of mistakes Neha. First, you can't just assume angle C is 65 degrees just because the they look like they are in the picture. Second, the Pythagoreom Theorem (a^2 + b^2 = c^2) only applies to right triangles.

I think you're going to need some trig functions to solve this. Here's what you know:

(Capital letters designate an angle, lowercase letters designate a side. Side c would be opposite angle C).

A= 65 dg

B = ?

C = ?

a = ?

b = 15

c = 11

I could be totally wrong here since its been a long time since I studied trig, but I believe the Law of Cosines could be used to find the value of a. Once you know that, the Law of Sines can be used to figure out B and C.

The Law of Cosines followed by the Law of Sines:

I stated the Law of Cosines as it's normally written which makes it confusing in this case because you only know A. So for you, it would be:

Hopefully this helps. And if I'm wrong, hopefully somebody will correct me.

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**Neha****Member**- Registered: 2006-10-11
- Posts: 173

ok this is what i did:

c^2 = a^2 + b^2 - 2ab cos P

A^ = 11^2 + 15^2 - 2(11)(15)cos 65dg

A^2 = 121 + 225 - 139.4640264

A^2 = 346 - 139.4640264

A^2 = 206.5359736

A = 14.37135949

A = 14.4

NEXT

14.4/sin65 = 15/sinB

sinB = 15sin65/14.4

SinB = 0.945952038

NEXT

14.4/sin65 = 11/sinC

sinC = 11sin65/14.4

sinC = 0.012106812

CORRECT

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**pi man****Member**- Registered: 2006-07-06
- Posts: 251

Looks good to me. Just one small mistake and then one more step. Your equation for calculating SIN(C) looks right but the answer is incorrect. It should be SIN(C) = .692320138.

You now know what the SIN(B) and SIN(C) are equal to so you can use the arcsin function to determine the angle.

B = arcsin(.945952038) = 71.07

C = arcsin(.692320138) = 43.81

Add those 2 together plus your 65 for Angle A and you get 179.88. Not quite 180 but I think that can be explained to rounding errors.

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