# finding the measure of an angle

• May 20th 2010, 11:58 AM
starrynight
finding the measure of an angle
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
• May 20th 2010, 12:03 PM
earboth
Quote:

Originally Posted by starrynight
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
Spoiler:
It's b)
• May 20th 2010, 12:03 PM
masters
Quote:

Originally Posted by starrynight
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: $a^2=b^2+c^2-2bc \cos A$
• May 20th 2010, 12:13 PM
starrynight
i get an answer of 145.5202602. is this correct?
• May 21st 2010, 02:24 AM
earboth
Quote:

Originally Posted by starrynight
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...°