Question

Write the six trigonometric functions for a right triangle with legs of length 21 and 28, is adjacent to the leg of length 28.​

Answer 1

Answer:

See below (along with attached triangle)

Step-by-step explanation:

We aren't given the hypotenuse, so let's solve that first:

$a^2+b^2=c^2\\21^2+28^2=c^2\\441+784=c^2\\1225=c^2\\35=c$

Now we can write the trigonometric functions:

$sin\theta=\frac{opposite}{hypotenuse}=\frac{21}{35}=\frac{3}{5}$

$cos\theta=\frac{adjacent}{hypotenuse}=\frac{28}{35}=\frac{4}{5}$

$tan\theta=\frac{opposite}{adjacent}=\frac{21}{28}=\frac{3}{4}$

$csc\theta=\frac{hypotenuse}{opposite}=\frac{35}{21}=\frac{5}{3}$

$sec\theta=\frac{hypotenuse}{adjacent}=\frac{35}{28}=\frac{5}{4}$

$cot\theta=\frac{adjacent}{opposite}=\frac{28}{21}=\frac{4}{3}$

I've attached a right triangle with the given information to help you visualize!

Answer 2

The six trigonometric functions for the right triangle are $\sin \theta = \frac{3}{5}$, $\cos \theta = \frac{4}{5}$, $\tan \theta = \frac{3}{4}$, $\cot \theta = \frac{4}{3}$, $\sec \theta = \frac{5}{4}$, $\csc \theta = \frac{5}{3}$.

Right triangles are modelled after Pythagorean theorem, which states that:

$r^{2} = x^{2}+y^{2}$ (1)

Where:

• $x$ - Adjacent leg.
• $y$ - Opposite leg.
• $r$ - Hypotenuse.

And trigonometric functions are defined below:

Sine

$\sin \theta = \frac{y}{r}$

Cosine

$\cos \theta = \frac{x}{r}$

Tangent

$\tan \theta = \frac{y}{x}$

Cotangent

$\cot \theta = \frac{x}{y}$

Secant

$\sec \theta = \frac{r}{x}$

Cosecant

$\csc \theta = \frac{r}{y}$

If we know that $x = 28$ and $y = 21$, then the six trigonometric functions are:

$r = \sqrt{28^{2}+21^{2}}$

$r = 35$

$\sin \theta = \frac{21}{35} = \frac{3}{5}$, $\cos \theta = \frac{28}{35} = \frac{4}{5}$, $\tan \theta = \frac{3}{4}$, $\cot \theta = \frac{4}{3}$, $\sec \theta = \frac{5}{4}$, $\csc \theta = \frac{5}{3}$

The six trigonometric functions for the right triangle are $\sin \theta = \frac{3}{5}$, $\cos \theta = \frac{4}{5}$, $\tan \theta = \frac{3}{4}$, $\cot \theta = \frac{4}{3}$, $\sec \theta = \frac{5}{4}$, $\csc \theta = \frac{5}{3}$.

To learn more on trigonometric functions, we kindly invite to check this verified question: https://brainly.com/question/20594759