Answer:
9) 5.8
10) 27.9
11) 37.1
12) 16.8
Step-by-step explanation:
For this you need to know SOH (sine = opposite/adj) CAH (cos = adj/hypo) and TOA (tan = opp/adj).
For 9, you have one side 15 and one angle 21 degrees. We can see that relative to the 21 degrees the side lengths, x and 15, are the Opposite and the Adjacent. So we label them "x=O" and "15=A". This means we have Tangent(21) = Opposite "x" /Adjacent "15"
We then evaluate tan21=x/15.
1) To get rid of the fraction multiply 15 on both sides to get 15*tan21=x.
2) Use a calculator to get the answer 5.8 (5.7579..)
For 10, it is the same process but with cosine. You have one side 19 and one angle 47 degrees. We can see that relative to the 21 degrees the side lengths, x and 19, are the Hypotenuse and the Adjacent. So we label them "x=H" and "19=A". This means we have Cosine(47) = Adjacent "19" / Hypotenuse "x"
We then evaluate cos47=19/x.
1) To get rid of the fraction multiply x on both sides to get x*cos47=19.
2) Divide by cos47 on both sides to isolate x. This will be x=47/cos21
3) Use a calculator to get the answer 27.9 (27.8593...)
For 11, refer to how I did question 9 on how it's tan68 = 15/x.
Then refer to question 10 on what to do if x is the denominator (isolate the x).
You should end up with x=15/tan68 which is 37.1 (37.1263...)
Finally for 12, it's the same but for sine (sin=opp/hyp).
You should get that the opp=15 and hypo=x.
That means sin63=15/x which is then x=15/sin63
Answer is 16.8 (16.834...)
