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mariarad [96]
3 years ago
8

I need help thank you

Mathematics
1 answer:
aliina [53]3 years ago
3 0

Answer:

Step-by-step explanation:

Use SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

we can find angle C  b/c the angles of a triangle always add to 180 , soo

180= C + 81 +63.5

35.5 = C

now that we have angle C and we know the Hyp we can use sin to find side g

where g = Opp and Hpy = 13.8 for this question

Sin(35.5) = Opp / 13.8

13.8*Sin(35.5) = Opp

8.0137 = Opp

g = 8.0137

next they ask for the area of the biggest triangle  ABC ( there are two smaller ones when you use D )

we can use 1/2 * base * height , but we don't know the base yet, even thou we do know the height.  

we can solve for line segment CD and DB and then add them for the side a .. or the base of the biggest triangle sooo.. CD = adj

Cos(35.5) = Adj / 13.8

13.8*Cos(35.5) = Adj

11.234794 =Adj

now solve for DB using cos again but with the other smaller triangle where  Adj = DB now

Cos(63.5) = Adj / 8.9

8.9*Cos(63.5) = Adj

3.971160

add these two Adjs together to get the total  'a' side

15.205954

now plug in side a as the base and g as the height of our biggest triangle

Area = 1/2 * 15.205954 * 8.0137

Area = 60.9159

rounded to 2 sig figs

Area = 60.92   :)   hope you get an "A"    :P

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There is a competition in the cinema to win free tickets. You must guess the ages of the four employees. Here are the clues: - W
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Answer:

Kirk is <u>28</u> years old, Brian is <u>36</u> years old, Matt is <u>18</u> years old, and the manager is <u>24</u> years old.

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Let k be Kirk's age.

Let b be Brian's age.

Let m be Matt's age.

Let m_{1} be the boss/manager's age.

From the information given, we can set up 4 equations:

k+b+m+m_{1}=106

k=2(m_{1}-10)

b=2m_{1}-12

m=\frac{1}{2}m_{1}+6

Rewrite the first equation, substituting k, b, and m in terms of m_{1} to get:

2(m_{1}-10)+(2m_{1}-12)+(\frac{1}{2}m_{1}+6)+m_{1}=106

Open up the parentheses using the distributive property (which is a(b-c)=ab-ac) and combine like terms to get:

5.5m_{1}-26=106

Add 26 to both sides to reach:

5.5m_{1}=132

Thus, m_{1}=24. Substitute 24 for m_{1} in the second, third, and fourth original equations to find that k=28, b=36, and m=18. Therefore, Kirk is <u>28</u> years old, Brian is <u>36</u> years old, Matt is <u>18</u> years old, and the manager is <u>24</u> years old. To check, you can add up all of the ages to get 106.

Hope this helps :)

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