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I'm studying for a test and I need help!

Question:
find the value of the three primary trigonometric ratios for angle A

A is opposite to 4 and adjacent to 8

three primary trig ratios = sin, tan and cos

for sin i looked at the answers and it's 1/square root of 5

how did they get this answer??!?

thanks!

2007-11-15 08:58:47 · 3 answers · asked by Besch 4 in Science & Mathematics Mathematics

ok so √80 = 4√5
HOW did you know that 4√5 = √80?
like if i were given that question how would i figure that out?

2007-11-15 09:09:47 · update #1

3 answers

the legs are 4 and 8 so the hypotenuse will be 4² + 8² = c² so c = √80 = 4√5
soh , cah , toa
sinA = 4/(4√5) = 1/√5 or √5 / 5
cosA = 8/(4√5) = 1/(2√5) or √5/10
tanA = 4/8 = 1/2
~~

when simplifying radical expressions like √80
you need to factor this number so that you get the biggest square number as one of the factors
so √80 = √( 16*5) = √16 * √5 === 4√5

~~

2007-11-15 09:06:26 · answer #1 · answered by ssssh 5 · 0 0

Soh Cah Toa
Sin = opposite / hypotenuse
Cos = adjacent / hypotenuse
Tan = opposite / adjacent

First, find the hypotenuse using the pyth.:
a^2 + b^2 = c^2
[4^2 + 8^2]^.5 = c
c = 4sqrt(5) (HYPOTENUSE)

Sin(A) = Opposite / Hypotenuse = 4 / 4sqrt(5) = 1 / sqrt(5)
Cos(A) = Adjacent / Hypotenuse = 8 / 4sqrt(5) = 2 / sqrt(5)
Tan(A) = Opposite / Adjacent = 4 / 8 = 1/2

2007-11-15 17:11:03 · answer #2 · answered by KEYNARDO 5 · 0 0

hypotenuse = sqrt(8^2+4^2) = sqrt(80) = 4Sqrt(5)
sin = side opposit /hypotenuse = 4/4sqrt(5) = 1/sqrt(5)

2007-11-15 17:09:01 · answer #3 · answered by ironduke8159 7 · 0 0

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