Answer:
1) The value of x= 0.0642
2) [tex]sin\theta=\frac{P}{H}=\frac{24}{25}[/tex]
[tex]cos\theta=\frac{B}{H}=\frac{7}{25}[/tex]
[tex]tan\theta=\frac{P}{B}=\frac{24}{7}[/tex]
[tex]cosec\theta=\frac{H}{P}=\frac{25}{24}[/tex]
[tex]cot\theta=\frac{B}{P}=\frac{7}{25}[/tex]
Step-by-step explanation:
1) Given : A right angle triangle with sides x and 10 and angle is 50°
To find : Value of x
Solution : Since, it is a right angle triangle
Therefore, we apply [tex]cos\theta=\frac{B}{H}[/tex]
Where Base = x, Hypotenuse= 10, angle = 50°
[tex]cos(50)=\frac{x}{10}[/tex]
[tex]0.642=\frac{x}{10}[/tex]
[tex]0.0642=x[/tex]
The value of x= 0.0642
2) Given : [tex]sec\theta=\frac{25}{7}[/tex]
To find : Value of [tex]sin\theta,cos\theta,tan\theta,cosec\theta,cot\theta[/tex]
Solution : We have given [tex]sec\theta=\frac{25}{7}[/tex]
[tex]sec\theta=\frac{H}{B}[/tex]
so, B= 7 , H=25
By Pythagoras theorem,
[tex]H^2=P^2+B^2[/tex]
[tex]25^2=P^2+7^2[/tex]
[tex]625-49=P^2[/tex]
[tex]\sqrt{576}=P^2[/tex]
[tex]P=24[/tex]
Now, P=24, B=7, H=25
[tex]sin\theta=\frac{P}{H}=\frac{24}{25}[/tex]
[tex]cos\theta=\frac{B}{H}=\frac{7}{25}[/tex]
[tex]tan\theta=\frac{P}{B}=\frac{24}{7}[/tex]
[tex]cosec\theta=\frac{H}{P}=\frac{25}{24}[/tex]
[tex]cot\theta=\frac{B}{P}=\frac{7}{25}[/tex]
