Respuesta :
Answer:
[tex]cos\theta=\frac{20}{29}[/tex]
Step-by-step explanation:
Problem:
[tex]sin\theta=\frac{21}{29},cos\theta=?,0^\circ<\theta<90^\circ[/tex]
Given:
[tex]sin\theta=\frac{opposite}{hypotenuse}=\frac{21}{29}[/tex]
[tex]cos\theta=\frac{adjacent}{hypotenuse}=\frac{x}{29}[/tex]
Solve for adjacent side:
[tex]a^2+b^2=c^2[/tex]
[tex]x^2+21^2=29^2[/tex]
[tex]x^2+441=841[/tex]
[tex]x^2=400[/tex]
[tex]x=20[/tex]
Final answer:
[tex]cos\theta=\frac{20}{29}[/tex]
The value [tex]\rm Cos\theta[/tex] is 20/29 and it can be determined by using the Pythagoras theorem.
Given that,
The value [tex]\rm Sin\theta[/tex] is 21/29,
Where [tex]0^{\circ}< \theta<90 ^{\circ}[/tex].
We have to determine,
The value of [tex]\rm Cos\theta[/tex]?
According to the question,
To determine the value of [tex]\rm Cos\theta[/tex] following all the steps given below.
The formula of [tex]\rm Sin\theta[/tex] is,
[tex]\rm Sin\theta =\dfrac{Perpendicular}{Hypotenuse}\\\\[/tex]
On comparing to the given value of [tex]\rm Sin\theta[/tex] is,
[tex]\rm Sin\theta =\dfrac{Perpendicular}{Hypotenuse}\\\\\rm Sin\theta =\dfrac{21}{29}\\\\[/tex]
Here, Hypotenuse = 29, and Perpendicular = 21
Then,
The formula of [tex]\rm Cos\theta[/tex] is,
[tex]\rm Cos\theta =\dfrac{Base}{Hypotenuse}\\\\[/tex]
Let, the base be x,
The value of base finding by using Pythagoras theorem,
[tex]\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[/tex]
The value of the base is 20.
Therefore,
[tex]\rm Cos\theta =\dfrac{Base}{Hypotenuse}\\\\\rm Cos\theta =\dfrac{20}{29}\\\\[/tex]
Hence, The value [tex]\rm Cos\theta[/tex] is 20/29.
For more details about Pythagoras theorem refer to the link given below.
https://brainly.com/question/13710437
