1.1.
Red and blue triangles are not similar: the ratio of the legs in the red triangle is 2/5, while the ratio in the blue one is 3/8. Therefore, they have different angles. As a result, the "hypotenuses" of the given figures are not really straight lines. In the top figure, the "hypotenuse" is slightly concave, and in the bottom figure, it is slightly convex. Therefore, these figures are not triangles (they are quadrilaterals), and their areas are different. In the top figure, the area is 32, in the bottom one, it is 33. So, we have difference in one square unit. The area of the “real” triangle is 32.5.

1.2.
The next three letters mean: Cosine is a ratio of Adjacent leg to Hypotenuse. The last three letters should be obvious.

1.3.
There are six trig functions. They represent all possible combinations of ratios of sides in a right triangle.

1.4.
Let x represents the height of Nick. Since the triangles are similar, we have
x/161 = 104/108. From here, x = 155 cm.

1.5.
1) b/c = cos A = sin B;   2) a/b = tan A = cot B;   3) b/a = cot A = tan B.

1.6.
1) sin A = 4/5;   2) cos A = 3/5;   3) tan A = 4/3;
4) sin B = 3/5;   5) cos B = 4/5;   6) tan B = 3/4.

1.7.
1) a = c·sin A = 2.38
2) b = a·tan B = 32.4
3) c = a/cos B = 7.45.

1.8.
sin 38° = 2.7/4.4 = 0.61;    sin 52° = 3.5/4.4 = 0.79;
cos 38° = 3.5/4.4 = 0.79;   cos 52° = 2.7/4.4 = 0.61;
tan 38° = 2.7/3.5 = 0.77;    tan 52° = 3.5/2.7 = 1.30.

1.9.
Let x represents the height of giraffe. Then x/4.8 = tan 32°. From here, x = 2.98 m.

1.10.
Let A represents the angle. Then cos A = 2/3.5 = 0.57. From here, A = 55°.

1.11.
Let x represents the altitude. Then x/120 = sin 37°. From here, x = 72 m.

1.12.
Let x represents the width of the river. Consider the picture

We have: tan 43° = y/x, tan 32° = y/(x + 10). Or, 0.93 = y/x, 0.62 = y/(x + 10). From the first equation we get: y = 0.93·x; from the second one: y = 0.62(x + 10). From here, 0.93·x = 0.62(x + 10). Solving for x, we get x = 20 m.