Mathematics: What is the trigonometric ratio for sin s ? express your answer, as a simplified fraction.

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What is the trigonometric ratio for sin s ? express

rudolph34

10.03.2022

For this case, we have that by definition:

Be a rectangular triangle and an "x" angle.

$Sine (x) = \frac {CO} {H}$

CO is the leg opposite the angle and H the hypotenuse

We want to find the Sine (S) according to the figure shown:

$Sine {S} = \frac {QR} {68}$

We do not have the opposite leg, we must apply the Pythagorean theorem, which states:

$H = \sqrt {(CO) ^ 2 + (CA) ^ 2}$

Where:

H: Hypotenuse

CO: Opposite leg

CA: Adjacent leg

In this case, we must find CO:

$CO = \sqrt {H ^ 2- (CA) ^ 2}$

Where:

$H = 68\\CA = 60$

Substituting:

$CO = \sqrt {68 ^ 2-60 ^ 2}\\CO = \sqrt {4624-3600}\\CO = \sqrt {1024}\\CO = 32$

So, we have:

$Sine (S) = \frac {32} {68}$

$Sine (S) = \frac {8} {17}$

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