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.
A ) B + C = 180.
A + 62 + 48 = 180, A = 70o.
sinB/b = sinA/a. b = ?.
21
To find side b, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.
The formula for the Law of Sines is:
a/sin(A) = b/sin(B) = c/sin(C)
Given that a = 18.2, B = 62°, and C = 48°, we plug these values into the formula:
18.2/sin(A) = b/sin(62°) = c/sin(48°)
To find b, we need to rearrange the formula to isolate b:
b = sin(B) * (a / sin(A))
Now we substitute the given values:
b = sin(62°) * (18.2 / sin(48°))
Using the trigonometric identities, we can calculate sin(62°) and sin(48°):
sin(62°) ≈ 0.8829
sin(48°) ≈ 0.7431
Substituting these values into the equation:
b ≈ 0.8829 * (18.2 / 0.7431)
b ≈ 21.589
Rounding this value to the nearest whole number, we find that b ≈ 22.
To find b in a triangle given the values of a, B, and C, 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 other words:
a/sin(A) = b/sin(B) = c/sin(C)
In this case, we are given a = 18.2, B = 62°, and C = 48°. We need to find b.
Let's substitute the given values into the formula and solve for b:
18.2/sin(A) = b/sin(B)
To solve for b, we need to find the value of sin(A).
To find sin(A), we can use the fact that the sum of angles in a triangle is 180°:
A + B + C = 180
A = 180 - B - C
A = 180 - 62 - 48
A ≈ 70
Now we can substitute the values into the formula:
18.2/sin(70) = b/sin(62)
To solve for b, we can cross-multiply:
18.2 * sin(62) = b * sin(70)
Next, we divide both sides of the equation by sin(70) to isolate b:
b = (18.2 * sin(62)) / sin(70)
Using a calculator, we find that sin(62) ≈ 0.8839 and sin(70) ≈ 0.9397. Substituting these values into the equation, we get:
b = (18.2 * 0.8839) / 0.9397
Simplifying further, we get:
b ≈ 17.073
Rounded to the nearest whole number, b ≈ 17.
Therefore, b ≈ 17.