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3 years ago

(07.01 HC)

Mathematics

1 answer:

KengaRu [80]3 years ago

8 0

Answer:

Sin x = 5/13

Cos y = 5/13

Sin x = cos y

Step-by-step explanation:

Recall: SOH CAH TOA

✔️Find sin x:

Sin x = Opp/Hyp

Opp = 5

Hyp = √(12² + 5²) (Pythagorean Theorem)

Hyp = 13

Sin x = 5/13

✔️Find cos y:

Cos y = Adj/Hyp

Hyp = 13 (calculated already)

Adj = 5

Cos y = 5/13

✔️Relationship between sin x and cos y is:

Sin x = cos y = 5/13

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Find the value of x and y

Natalija [7]

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

What does the information want:

value of x
value of y

Let's gather some information:

ΔA'BC' and ΔABC are similar triangles

⇒ Angle B is shared by both triangles

⇒ Angle A' and A are the same, as they are both on parallel

lines, A'C' and AC, and both angles are formed with the

same line AB

⇒ by the Angle-Angle Theorem*, they are similar triangles

If they are similar triangles:

⇒ their side lengths are proportional to each other

let's find x's value

⇒ let's set up a proportion

$\frac{A'B}{AB} =\frac{A'C'}{AC} \\\frac{30}{x+30} =\frac{14}{22} \\14(x+30) = 30*22\\14x + 420 = 660\\14x = 240\\x = 17.143$

let's find y's value

⇒ let's set up a proportion

$\frac{BC'}{BC} =\frac{A'C'}{AC} \\\frac{y}{y+15} =\frac{14}{22} \\22y=14(y+15)\\22y=14y+210\\8y=210\\y=26.25$

Answer:

x= 17.143
y = 26.25

Hope that helps!

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