Final answer:
To find the measure of angle A in triangle ABC using the sine ratio, use the formula sin(A) = opposite/hypotenuse. Solve for the value of sin(A) and then find the inverse sine to determine the measure of angle A = 25 degrees. So, the correct answer is B) 25 degrees.
Step-by-step explanation:
To find the measure of angle A in triangle ABC using the sine ratio, we can use the formula sin(A) = opposite/hypotenuse.
Since we are given the side lengths AB=6 and BC=5, we can find the length of AC using the Pythagorean theorem: AC = sqrt(AB² + BC²) = sqrt(6² + 5²) = √(36 + 25) = √(61).
Now, we can use the sine ratio formula to find the measure of angle A: sin(A) = opposite/hypotenuse = BC/AC = 5/√(61).
Taking the inverse sine (sin⁻¹) of this value will give us the angle A: A = sin⁻¹(5/√(61)).
Using a calculator, we find that A ≈ 25 degrees.
Thus, the correct answer is B) 25 degrees.
Question: Consider triangle ABC with side lengths AB= 6, BC= 5, and an angle of B maeasure 65 degrees. Find the measure of angle A using the sine ratio.
Options:
A) 65 degrees
B) 25 degrees
C) 115 degrees
D) 90 degrees