Question

Given that A = 25°, B = 43°, and c = 17, solve triangle ABC. Round to the nearest hundredth. What are the values of angles C, sides b, and side a?

a) C = 112°, b = 7.5, a = 12.5
b) C = 1120°, b = 12.5, a = 7.75
c) C = 220°, b = 12.5, a = 7.75
d) C = 22°, b = 7.5, a = 12.5

Answer 1

To solve triangle ABC, we can use the sine rule to find the values of angle C and sides b and a. Angle C is approximately 112°, side b is approximately 7.5, and side a is approximately 12.5.

Step-by-step explanation:

To solve triangle ABC, we can use the sine rule. The sine rule states that the ratios of the lengths of the sides of a triangle to the sine of their opposite angles are equal:

a/sin(A) = b/sin(B) = c/sin(C)

Given that A = 25°, B = 43°, and c = 17, we can plug these values into the sine rule equation:

a/sin(25°) = 17/sin(43°)

Now we can solve for side 'a' by cross multiplying and then dividing:

a = (17 * sin(25°)) / sin(43°)

Using a calculator, we find that a ≈ 12.5. So the value of side 'a' is approximately 12.5. Similarly, using the sine rule, we can find the values of angle C and side b. Angle C is equal to 180° - A - B, so C ≈ 180° - 25° - 43° ≈ 112°. And side b can be found using the sine rule equation:

b = (17 * sin(43°)) / sin(25°)

Using a calculator, we find that b ≈ 7.5. So the value of side b is approximately 7.5. Therefore, the correct answer is (a) C = 112°, b = 7.5, a = 12.5.