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.
![$\sin \theta=\frac{\text { opposite }}{\text { hypotenuse }}](https://img.qammunity.org/2021/formulas/mathematics/middle-school/ck8tw9nzo6g2pfflce34lm7af2bste641x.png)
![$\sin C=(AB)/(BC)](https://img.qammunity.org/2021/formulas/mathematics/college/xkdn0p46z3jq5i2hflnzqmk9d94fakrqge.png)
![$\sin 45^\circ=(x)/(6.4)](https://img.qammunity.org/2021/formulas/mathematics/college/okmuweq50m79mp54yub2cnaqyjhagdar1y.png)
![$(1)/(√(2) ) =(x)/(6.4)](https://img.qammunity.org/2021/formulas/mathematics/college/ohrdps7xnc1l6qifkcc0ptzrbyyrip6waw.png)
Multiply 6.4 on both sides, we get
![$(6.4)/(√(2) )=x](https://img.qammunity.org/2021/formulas/mathematics/college/oub0d1rwtfa2kqyor9itd7c0x61s0sznpq.png)
x = 4.5
The value of x is 4.5.
Question 5:
The given triangle is a right triangle.
Using trigonometric formulas for a right triangle.
![$\sin \theta=\frac{\text { opposite }}{\text { hypotenuse }}](https://img.qammunity.org/2021/formulas/mathematics/middle-school/ck8tw9nzo6g2pfflce34lm7af2bste641x.png)
![$\sin E=(EF)/(DF)](https://img.qammunity.org/2021/formulas/mathematics/college/w0m85u00d847ywwx3txyn74u4xz9zohy00.png)
![$\sin 60^\circ=(x)/(18)](https://img.qammunity.org/2021/formulas/mathematics/college/ikiv1kw3zpb98jn0a7db16dni7cx3zyuen.png)
![$(\sqrt3)/(2) =(x)/(18)](https://img.qammunity.org/2021/formulas/mathematics/college/8pqeh10194f59ahogjvcodojxxfsxj92jh.png)
Multiply 18 on both sides, we get
x = 15.6
The value of x is 15.6.