Please help me I need this to be done it would mean a lot :)

Answers:

16. sin(A) = a/12

17. tan(A) = a/9

18. sin(B) = 3/4    (reduced from 9/12)

19. cos(B) = a/12

Explanation:

The sine of an angle is equal to the ratio of the opposite side over the hypotenuse. For reference angle A, the opposite side is BC = a. The hypotenuse is always the longest side. The hypotenuse is AB = 12.

sin(angle) = opposite/hypotenuse

sin(A) = BC/AB

sin(A) = a/12

Similarly,

sin(B) = opposite/hypotenuse = AC/AB = 9/12 = 3/4.

Tangent is the ratio of opposite over adjacent

tan(angle) = opposite/adjacent

tan(A) = BC/AC

tan(A) = a/9

Cosine is the ratio of adjacent over hypotenuse

cos(angle) = adjacent/hypotenuse

cos(B) = BC/AB

cos(B) = a/12

we see that this is the same result as sin(A). It turns out that sin(A) = cos(B) if and only if A+B = 90. In other words, the sin(A) = cos(B) when A and B are the acute angles of a right triangle.

Side note: you could use the Pythagorean theorem to solve for the value of 'a'. All of this assumes that triangle ACB is a right triangle.

70 minutes.

Step-by-step explanation:

You would say 40, but think, he has to walk back and get the other kid by himself. Double it. Then subtract ten minutes bc hes not walking back for another kid.