Question

Use the stated variant of the Law of Cosines, b2=a2+c2−2ac⋅cosB
𝑏
2
=
𝑎
2
+
𝑐
2
−
2
𝑎
𝑐
⋅
cos
⁡
𝐵
, to find the value of side b in a right triangle, where a=3
𝑎
=
3
, c=5
𝑐
=
5
, and B=53.13
𝐵
=
53.13
. Round your answer to the nearest whole number.(1 point)
b=
𝑏
=

Answer 1

Use the Law of Cosines:
b^2 = a^2 + c^2 − 2ac cos B
b^2 = 3^2 + 5^2 − 2(3)(5)cos(53.13°)
cos(53.13°) = 0.6 (3-4-5 triangle), so
b^2 = 9 + 25 − 30(0.6) = 34 − 18 = 16
b = √16 = 4

Rounded to the nearest whole number: b = 4.