Question

a right triangle has side lengths 3, 4, and 5 as shown below. Use these lengths to find sinL, tanL, cosL​

Answer 1

Answer:

Step-by-step explanation:

I like to remember the three trigonometric equations with the following mnemonic device: SOH CAH TOA

SOH = $sin(x) = \frac{opposite}{hypotenuse}$

CAH = $cos(x) = \frac{adjacent}{hypotenuse$

TOA = $tan(x) = \frac{opposite}{adjacent}$

The $opposite$ length is the side length that is directly across (or opposite) of the given angle.

The $adjacent$ length is the side length that is right next to the given angle (but not the hypotenuse).

For this case, $sin(L)$ is going to be the opposite side length over the hypotenuse, which is $\frac{3}{5}$.

$tan(L)$ is going to be the opposite side length over the adjacent side length, which is $\frac{3}{4}$.

$cos(L)$ is going to be the adjacent side length over the hypotenuse, which is $\frac{4}{5}$.

Answer 2

A right triangle has side lengths 3, 4, and 5. so, sinL = 3/5, tanL= 4/5, cosL​ = 3/4.

What are the six trigonometric ratios?

Trigonometric ratios for a right-angled triangle are from the perspective of a particular non-right angle.

In a right-angled triangle, two such angles are there which are not right-angled(not of 90 degrees).

The slanted side is called the hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called the base.

From that angle (suppose its measure is θ),

$\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}$

A right triangle has side lengths 3, 4, and 5.

$\sin(L) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\\\sin(L) = \dfrac{3}{5}$

$cos(L) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\cos(L) = \dfrac{4}{5}$

$tan(L) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\tan(L) = \dfrac{3}{4}$

Learn more about trigonometric ratios here:

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