Answer:
tan A = 0.43
tan B = 2.34
Explanation:
"tangent" is a trig ratio. If you have a right triangle, then you can do right triangle trigonometry.
First, let's look at a right triangle. The longest side is opposite the right angle (square angle, 90° angle it's marked with a little square) that is called the hypotenuse. You need hypotenuse for sine and cosine. So we won't use hypotenuse today (still good to know tho')
Then there are the two legs of the right triangle. They make up the right angle. If you are standing at one of the smaller angles one of the legs is just beside you, making up the angle. The other leg is way across the triangle on the opposite side of the triangle.
So from angle A, the 32 is the OPPOSITE side. And the 75 is the leg right next to angle A. "Right next to" is called ADJACENT. The 75 is the ADJACENT side.
Tangent is the ratio of the OPPOSITE side to the ADJACENT side.
Like this:
tan A = OPP/ADJ
tan A = 32/75
tan A = 0.426666...
rounding, we get:
tan A = 0.43
From angle B (imagine yourself standing right there at angle B) the ADJACENT side (right next to you) is 32. And the OPPOSITE side is 75
Now the tangent ratio is slightly different--
tan B = OPP/ADJ
tan B = 75/32
tan B = 2.34375
rounding,
tan B = 2.34