In triangle ABC, a = 3, b = 5, and c = 7. Find the approximate value of angle A.

22°
38°
142°
158°

Question

In triangle ABC, a = 3, b = 5, and c = 7. Find the approximate value of angle A.

22°
38°
142°
158°

johnweldon1993 · Answer

We can use the law of cosine here

we know

$$\large a^2 = b^2 + c^2 - 2bc \times cos(A)$$

So since we want to solve for A we need to rearrange this into

$$\large A = \arccos(\frac{a^2 - b^2 - c^2}{-2bc})$$

So just plug in everything you have and solve

anonymous · Answer

what is arccos

johnweldon1993 · Answer

the inverse cosine function

also known as $\large cos^{-1}$

anonymous · Answer

okay and i just got .92

anonymous · Answer

btw i dont have an actual calculator

johnweldon1993 · Answer

The 0.92 is what you get when you do everything in the parenthesis...now you just need the inverse cosine of that

Which, since you dont have a calculator...comes out to 21.786

johnweldon1993 · Answer

So that would lead to your "approximate" answer to be 22 degrees