Where Did I Go Wrong with the Cosine Formula?

In summary, the conversation is about finding the length of side a in a triangle using the formula -a2 = b2 + c2 - 2bc cos A, where angle A is 350 degrees, side b is 7 cm, and side c is 3 cm. The person initially made a mistake by multiplying 16 by cos 35 and taking the square root, but the correct method is to first multiply 42 by cos 35 and then subtract that from 58. Thanks to the explanation, the person now understands where they went wrong.
  • #1
Gringo123
141
0
I got this question wrong and I'm hoping someone can explain to me where I went wrong.

In a triangle...
angle A = 350
side b = 7 cm
side c = 3 cm

I need to find side a which is the side opposite angle A.

The formaula to use is -a2 = b2 + c2 - 2bc cos A
so, with the figures plugged in that comes out as...

a2 = 72 + 32 - 2 x 3 x 7 cos 35

which comes to...

a2 = 58 - 42 cos 35

SO FAR, I KNOW THAT IS CORRECT. I seem to have made the mistake at this point. I multiplied 16 (58-42) by cos 35 and took the square root of the answer, which gave me 3.62 cm.
However, apparently the right answer is 4.86 cm.
What did I do wrong?
 
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  • #2
Gringo123 said:
I multiplied 16 (58-42) by cos 35 and took the square root of the answer, which gave me 3.62 cm.
However, apparently the right answer is 4.86 cm.
What did I do wrong?
58 - 42 cos 35 ≠ (58 - 42) cos35

58 - 42 cos 35 = 58 - (42 cos35)



Multiply 42 by cos35, then subtract that from 58.
 
  • #3
That's brilliant! Thanks a lot Doc!
 

FAQ: Where Did I Go Wrong with the Cosine Formula?

1. What is the Cosine formula used for?

The Cosine formula is used to find the length of a side or the measure of an angle in a triangle. It is also used to solve problems involving vectors and coordinate geometry.

2. How is the Cosine formula written?

The Cosine formula is written as c^2 = a^2 + b^2 - 2ab cos(C), where c represents the length of the side opposite angle C and a and b represent the lengths of the other two sides.

3. When should the Cosine formula be used?

The Cosine formula should be used when you know the lengths of two sides and the measure of the included angle in a triangle. It can also be used when you know the coordinates of two points in a coordinate plane.

4. What are the limitations of the Cosine formula?

The Cosine formula can only be used in right triangles or when the Law of Cosines is applied in non-right triangles. It also assumes that you know the measure of at least one angle in the triangle.

5. How can the Cosine formula be used in real-life applications?

The Cosine formula has many practical applications, such as calculating distances between points on a map or in navigation and surveying. It is also used in physics and engineering to analyze forces and motion.

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