Answer:
Exact form: x = [tex]\frac{10.8}{sin(57)}[/tex]
Rounded to the Nearest Tenth: x = 12.9
Step-by-step explanation:
In the right-angled triangle, we can use the trigonometry functions to find the length of a side or a measure of an angle
In the given figure
∵ ∠C is the right angle
∴ ΔACB is a right triangle
∵ m∠B = 57°
∵ AC = 10.8
∵ AC is the opposite side of ∠B
∵ AB is opposite to the right angle
∴ AB is the hypotenuse
∵ AB = x
→ We can use the function sine to find x
∵ sin∠B = [tex]\frac{opposite}{hypotenuse}[/tex]
∴ sin∠B = [tex]\frac{AC}{AB}[/tex]
→ Substitute the values of ∠B, AC, and AB in the rule of sine above
∴ sin(57°) = [tex]\frac{10.8}{x}[/tex]
→ By using cross multiplication
∵ x × sin(57°) = 10.8
→ Divide both sides by sin(57°)
∴ x = [tex]\frac{10.8}{sin(57)}[/tex]
∴ x = 12.87752356
→ Round your answer to the nearest tenth
∴ x = 12.9
Exact form: x = [tex]\frac{10.8}{sin(57)}[/tex]
Rounded to the Nearest Tenth: x = 12.9
