Question

50 Points

PLEASEEEEE HELPPP
Trigonometry SIN/CON
I need help for numbers 22, 24, 26, 28, 30, 32, 34, 36

Answer 1

Answers are in bold.

22. b/c

24. sqrt(17)/17

26. 1/4

28. sqrt(17)/17

30. 1/2

32. sqrt(2)/2

34. sqrt(3)/2

36. Approximately 5.4077 units

=====================================================

Step-by-step explanation:

Problem 22

To get the cosine ratio, we divide the adjacent over hypotenuse.

cos(angle) = adjacent/hypotenuse

cos(x) = b/c

----------------------------------

Problem 24

To get the sine ratio, we divide opposite over hypotenuse.

`\sin\left(\text{angle}\right) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin\left(\text{x}\right) = (2)/(2√(17))\\\\\sin\left(\text{x}\right) = (1)/(√(17))\\\\\sin\left(\text{x}\right) = (1*√(17))/(√(17)*√(17))\\\\\sin\left(\text{x}\right) = \boldsymbol{(√(17))/(17)}\\\\`

In the fourth step, I multiplied top and bottom by sqrt(17) to rationalize the denominator.

----------------------------------

Problem 26

tan(angle) = opposite/adjacent

tan(x) = 2/8

tan(x) = 1/4

----------------------------------

Problem 28

cos(y) = sin(x) in this case. The general rule is that sin(A) = cos(B) if and only if A+B = 90.

Therefore the answer is exactly identical to problem 24.

----------------------------------

Problem 30

sin(30) = 1/2 is something you either memorize or look up on a reference chart, or use the unit circle. Alternatively, you can use a 30-60-90 triangle template.

----------------------------------

Problem 32

`\sin\left(45^(\circ)\right) = \boldsymbol{(√(2))/(2)}\\\\` is something you memorize or have on a reference sheet. You could also use a 45-45-90 triangle.

----------------------------------

Problem 34

`\cos\left(30^(\circ)\right) = \boldsymbol{(√(3))/(2)}\\\\` is similar to problems 30 and 32 in that you should memorize this or have it on a reference sheet. You could use a 30-60-90 triangle template here.

----------------------------------

Problem 36

Let x be the length of side AC.

Use the tangent ratio to find x.

tan(angle) = opposite/adjacent

tan(B) = AC/AB

tan(31) = x/9

x = 9*tan(31)

x = 5.4077 approximately