Find b, given that a = 18.2, B = 62°, and C = 48°. Round answers to the nearest whole number. Do not use a decimal point or extra spaces in the answer or it will be marked incorrect.
17.1
To find b, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.
In this case, we have the following information:
a = 18.2 (side opposite angle A)
B = 62°
C = 48°
We can use the following formula:
sin(A)/a = sin(B)/b
Plugging in the known values:
sin(62°)/18.2 = sin(48°)/b
To find b, we need to solve for it. First, let's find sin(62°) and sin(48°). Using a calculator, we find that sin(62°) ≈ 0.8839 and sin(48°) ≈ 0.7431.
Now we can plug these values back into the equation:
0.8839/18.2 = 0.7431/b
To solve for b, we can cross-multiply:
0.8839 * b = 18.2 * 0.7431
Dividing both sides by 0.8839:
b ≈ (18.2 * 0.7431) / 0.8839
Using a calculator, we find that b ≈ 15.302
Rounding to the nearest whole number, b ≈ 15.
Therefore, b is approximately 15.