Answer:
The value of x is:
[tex]x=5.32[/tex]
Step-by-step explanation:
We have the hypotenuse of the triangle : [tex]7.8~\text{cm}[/tex]
And we have the unknown side opposite to the angle given : [tex]x~\text{cm}[/tex]
And finally, the angle itself is: [tex]43^{\circ}[/tex]
We can make use of the sine trigonometric ratio here:
[tex]\sin{\theta}= \frac{O}{H}[/tex]
Where O is the opposite side to the angle, and H the hypotenuse.
Substitute the values given:
[tex]\sin{43^{\circ}}=\frac{x}{7.8}[/tex]
Multiply both sides by 7.8:
[tex]\sin{43^{\circ}} \times 7.8=\frac{x}{7.8} \times 7.8\\\\\sin{43^{\circ}} \times 7.8=x[/tex]\
Find the value of x:
[tex]x=5.32[/tex]
