finding the measure of an angle

Feb 2008
17
0
florida
if a triangle has the sides a=412, b=324, c=636, what is the measure of angle A?

we can choose from these answers:

a) 119.1
b) 34.5
c) 48.7
d) 26.4
e) none of these
 

earboth

MHF Hall of Honor
Jan 2006
5,854
2,553
Germany
if a triangle has the sides a=412, b=324, c=636, what is the measure of angle A?

we can choose from these answers:

a) 119.1
b) 34.5
c) 48.7
d) 26.4
e) none of these
1. Draw a sketch.

2. Use the Cosine rule. And then show your work. We'll check if everything is OK.

3
It's b)
 

masters

MHF Helper
Jan 2008
2,550
1,187
Big Stone Gap, Virginia
if a triangle has the sides a=412, b=324, c=636, what is the measure of angle A?

we can choose from these answers:

a) 119.1
b) 34.5
c) 48.7
d) 26.4
e) none of these
Hi starrynight,

Use the law of cosines: \(\displaystyle a^2=b^2+c^2-2bc \cos A\)
 
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earboth

MHF Hall of Honor
Jan 2006
5,854
2,553
Germany
i get an answer of 145.5202602. is this correct?
Obviously not:

1. According to the Cosine rule an angle greater than 90° must be opposite the largest side in the triangle. That is the side c and not the side a, which is opposite the angle at A.

2. You probably have forgotten about the negative sign in the denominator and therefore the correct result would be:

180° - 145.5202602° = 34.479...°