We can use the law of cosines for these.
The law of cosines says: c2 = a2 + b2 - 2ab cos C , where C is the angle opposite side c .
In the first problem, we want to know the measure of the angle across from the side that is 4 cm.
42 = 32 + 52 - 2(3)(5)cos B
Simplify.
16 = 9 + 25 - 30 cos B
16 = 34 - 30 cos B
Subtract 34 from both sides.
-18 = -30 cos B
Divide both sides by -30 .
0.6 = cos B
Take the inverse cosine of both sides.
acos( 0.6 ) = B
53.13° ≈ B
For the second problem, note that the smallest angle is opposite the smallest side, and the largest angle is opposite the largest side. ( You can look at this to see why. )
So...the angle across from the side that is 5 cm will be the smallest.
We can find the measure of this angle, " A " , with the law of cosines again.
52 = 92 + 122 - 2(9)(12) cos A
25 = 225 - 216 cos A
200/216 = cos A
acos(200/216) = A
22.19º ≈ A
And the largest angle is across from the 12 cm side... " C " .
122 = 52 + 92 - 2(5)(9) cos C
144 = 106 - 90 cos C
38/ - 90 = cos C
114.98º ≈ C
You can copy and paste the intersection symbol, like this one in the problem: ∩
If there is such a symbol for what you need, you can usually find it in a google search.
If you can't find one....you can use LaTeX to make most symbols. For example, typing " \cap " into LaTeX makes an ∩ . If you can't find the right symbol in the buttons at the top...the code you need might be in this post or this post.