Question

Solve the triangle. a=6,b=4,C=70° c≈ __ (Round to two decimal places as needed.) A≈ __ (Round to one decimal place as needed.) B≈ __° (Round to one decimal place as needed.)

Answer 1

To solve the triangle, we can use the Law of Sines to find all the missing values. Angle A is approximately 110°, side c is approximately 4.76 units long, and side a is approximately 6.4 units long.

Step-by-step explanation:

To solve the triangle, we can use the Law of Sines. Firstly, we can find angle A by using the formula: A = 180° - B - C. Thus, A = 180° - 70° - B = 110° - B.

Next, we can use the Law of Sines to find side c: c/sinC = b/sinB. Plugging in the values, we have c/sin70° = 4/sin(B). Solving for sin(B) and B, we find B ≈ 48.7° and c ≈ 4.761.

Finally, we can find side a by using the Law of Sines again: a/sinA = c/sinC. Plugging in the values, we have a/sin(110° - B) = 4.761/sin70°. Solving for a, we find a ≈ 6.4.