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.
