Answer:
x = 33.4
Step-by-step explanation:
The diagram shows right triangle ABC, with the angle at vertex A marked as 'x', and side lengths BC = 3.3 and AC = 6.
As we have been given the lengths of the side opposite angle x and the hypotenuse, we can use the sine trigonometric ratio to find the value of x.
[tex]\boxed{\begin{array}{l}\underline{\textsf{Sine trigonometric ratio}}\\\\\sf \sin(\theta)=\dfrac{O}{H}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$\theta$ is the angle.}\\\phantom{ww}\bullet\;\textsf{O is the side opposite the angle.}\\\phantom{ww}\bullet\;\textsf{H is the hypotenuse (the side opposite the right angle).}\end{array}}[/tex]
In this case:
- θ = x°
- O = BC = 3.3
- H = AC = 6
Substitute the values into the sine ratio and solve for x:
[tex]\sin x^{\circ}=\dfrac{3.3}{6} \\\\\\ \sin x^{\circ}=0.55 \\\\\\ x^{\circ}=\sin^{-1}(0.55) \\\\\\ x^{\circ}=33.36701296923...^{\circ}\\\\\\ x=33.4\; \sf (nearest\;tenth)[/tex]
Therefore, the value of x rounded to the nearest tenth is:
[tex]\LARGE\boxed{\boxed{x=33.4}}[/tex]
