Answer:
Exact form: x =
Rounded to the Nearest Tenth: x = 12.9
Step-by-step explanation:
<em>In the right-angled triangle, we can use the trigonometry functions to find the length of a side or a measure of an angle</em>
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 =
∴ sin∠B =
→ Substitute the values of ∠B, AC, and AB in the rule of sine above
∴ sin(57°) =
→ By using cross multiplication
∵ x × sin(57°) = 10.8
→ Divide both sides by sin(57°)
∴ x =
∴ x = 12.87752356
→ Round your answer to the nearest tenth
∴ x = 12.9
Exact form: x =
Rounded to the Nearest Tenth: x = 12.9