A triangle has the length of AB = 125ft, BC = 85ft. The size if angle C is 63°. Determine the length of AC.
use the law of sines to find ∠A (opposite BC)
subtract ∠C and ∠A from 180º to find ∠B (opposite AC)
use the law of sines (again) to find AC (opposite ∠B)
sinA/85 = sin63/125
A = 37 degrees.
B = 180-37-63 = 80 degrees.
AC/sin80 = 125/sin63.
AC =
To find the length of AC in the given triangle, we can use the Law of Cosines. The Law of Cosines states that in a triangle with side lengths a, b, and c, and angle C opposite side c, the following formula can be used:
c^2 = a^2 + b^2 - 2ab * cos(C)
Let's plug in the given values:
AC^2 = AB^2 + BC^2 - 2 * AB * BC * cos(C)
AC^2 = (125ft)^2 + (85ft)^2 - 2 * 125ft * 85ft * cos(63°)
AC^2 = 15625ft^2 + 7225ft^2 - 2 * 125ft * 85ft * cos(63°)
AC^2 = 22850ft^2 - 21375ft * cos(63°)
Now, we can calculate the length of AC using a scientific calculator or a trigonometric table to find the value of cos(63°). After calculating the value of cos(63°), substitute it in the equation and find the square root of AC^2 to get the length of AC.