Question

Solve the triangle. (A = 46°), (a = 34), (b = 27)

a) (B = 34.8°), (C = 99.2°), (c ≈ 28)
b) (B = 34.8°), (C = 119.2°), (c ≈ 37.3)
c) Cannot be solved
d) (B = 34.8°), (C = 99.2°), (c ≈ 46.7)

Answer 1

To solve the given triangle, use the Law of Sines to find the angles B and C. Then, determine the value of side c using the information provided. The correct answer is option a) (B = 34.8°), (C = 99.2°), (c ≈ 28).

Step-by-step explanation:

To solve the triangle, we can use the Law of Sines, which states that the ratios of the lengths of the sides of a triangle are equal to the ratios of the sines of their opposite angles. Given A = 46°, a = 34, and b = 27, we can solve for B and C using the Law of Sines.

Step 1: Use the Law of Sines to solve for B: sin(B)/27 = sin(46°)/34. Cross-multiply and solve for sin(B): sin(B) ≈ (27*sin(46°))/34. Take the arcsine of this value to find B: B ≈ arcsin((27*sin(46°))/34).

Step 2: Use the Law of Sines to solve for C: sin(C)/34 = sin(46°)/27. Cross-multiply and solve for sin(C): sin(C) ≈ (34*sin(46°))/27. Take the arcsine of this value to find C: C ≈ arcsin((34*sin(46°))/27).

Therefore, the triangle can be solved as (B ≈ arcsin((27*sin(46°))/34), C ≈ arcsin((34*sin(46°))/27), c ≈ 28). So the correct answer is (B = 34.8°), (C = 99.2°), (c ≈ 28), which is option a).