Question

Given that Sine theta = StartFraction 21 Over 29 EndFraction, what is the value of cosine theta, for 0 degrees less-than theta less-than 90 degrees? Negative StartRoot StartFraction 20 Over 29 EndFraction EndRoot Negative StartFraction 20 Over 29 EndFraction StartFraction 20 Over 29 EndFraction StartRoot StartFraction 20 Over 29 EndFraction EndRoot.

Answer 1

Answer:

$cos\theta=\frac{20}{29}$

Step-by-step explanation:

Problem:

$sin\theta=\frac{21}{29},cos\theta=?,0^\circ$

Given:

$sin\theta=\frac{opposite}{hypotenuse}=\frac{21}{29}$

$cos\theta=\frac{adjacent}{hypotenuse}=\frac{x}{29}$

Solve for adjacent side:

$a^2+b^2=c^2$

$x^2+21^2=29^2$

$x^2+441=841$

$x^2=400$

$x=20$

Final answer:

$cos\theta=\frac{20}{29}$

Answer 2

The value  $\rm Cos\theta$ is 20/29 and it can be determined by using the Pythagoras theorem.

Given that,

The value  $\rm Sin\theta$ is 21/29,

Where $0^{\circ}< \theta$.

We have to determine,

The value of $\rm Cos\theta$?

According to the question,

To determine the value of $\rm Cos\theta$ following all the steps given below.

The formula of $\rm Sin\theta$ is,

$\rm Sin\theta =\dfrac{Perpendicular}{Hypotenuse}$

On comparing to the given value of  $\rm Sin\theta$ is,

$\rm Sin\theta =\dfrac{Perpendicular}{Hypotenuse}\\\\\rm Sin\theta =\dfrac{21}{29}$

Here, Hypotenuse = 29, and Perpendicular = 21

Then,

The formula of $\rm Cos\theta$ is,

$\rm Cos\theta =\dfrac{Base}{Hypotenuse}$

Let, the base be x,

The value of base finding by using Pythagoras theorem,

$\rm {(Hypotenuse)}2 = (Perpendicular)^2+ (Base)^2\\\\ (29)^2 = (21)^2 + (x)^2\\\\841= 441 +x^2\\\\x^2 = 841-441\\\\x^2 = 400\\\\x = 20$

The value of the base is 20.

Therefore,

$\rm Cos\theta =\dfrac{Base}{Hypotenuse}\\\\\rm Cos\theta =\dfrac{20}{29}$

Hence, The value  $\rm Cos\theta$ is 20/29.

For more details about Pythagoras theorem refer to the link given below.

brainly.com/question/13710437