In triangle ABC, side AB=210cm , side BC=180cm and angle B=54° . find the length of side AC?
To find the length of side AC, we can use the Law of Cosines. The Law of Cosines states that for a triangle with sides a, b, and c, and angle C opposite side c, the following equation holds:
c^2 = a^2 + b^2 - 2ab*cos(C)
Let side AC = c. We know that side AB = 210 cm and side BC = 180 cm. We also know that angle B = 54°.
Plugging these values into the Law of Cosines equation, we get:
c^2 = (210 cm)^2 + (180 cm)^2 - 2(210 cm)(180 cm)*cos(54°)
Calculating this:
c^2 = 44100 cm^2 + 32400 cm^2 - 2(210 cm)(180 cm)*0.58779
c^2 = 44100 cm^2 + 32400 cm^2 - 220500 cm^2 * 0.58779
c^2 = 44100 cm^2 + 32400 cm^2 - 129441.9 cm^2
c^2 = 6358.1 cm^2
Taking the square root of both sides, we find that:
c ≈ 79.76 cm
So, the length of side AC is approximately 79.76 cm.