Question 4: The value of x is 4.5.
Question 5: The value of x is 15.6.
Solution:
Question 4:
The given triangle is a right triangle.
Using trigonometric formulas for a right triangle.
[tex]$\sin \theta=\frac{\text { opposite }}{\text { hypotenuse }}[/tex]
[tex]$\sin C=\frac{AB}{BC}[/tex]
[tex]$\sin 45^\circ=\frac{x}{6.4}[/tex]
[tex]$\frac{1}{\sqrt{2} } =\frac{x}{6.4}[/tex]
Multiply 6.4 on both sides, we get
[tex]$\frac{6.4}{\sqrt{2} }=x[/tex]
x = 4.5
The value of x is 4.5.
Question 5:
The given triangle is a right triangle.
Using trigonometric formulas for a right triangle.
[tex]$\sin \theta=\frac{\text { opposite }}{\text { hypotenuse }}[/tex]
[tex]$\sin E=\frac{EF}{DF}[/tex]
[tex]$\sin 60^\circ=\frac{x}{18}[/tex]
[tex]$\frac{\sqrt3}{2} =\frac{x}{18}[/tex]
Multiply 18 on both sides, we get
x = 15.6
The value of x is 15.6.
