To find the measure of side AB, we can use the Law of Cosines.
The Law of Cosines states:
c^2 = a^2 + b^2 - 2ab cos(C)
Where:
- a, b, and c are the sides of the triangle
- A, B, and C are the angles opposite to the sides a, b, and c, respectively
Since we want to find the measure of side AB (which is opposite to angle C), we have:
c^2 = a^2 + b^2 - 2ab cos(C)
AB^2 = AC^2 + BC^2 - 2(AC)(BC) cos(55°)
Given that AC = 68 and BC = 68, we can substitute these values into the formula:
AB^2 = 68^2 + 68^2 - 2(68)(68) cos(55°)
AB^2 = 4624 + 4624 - 2(4624) cos(55°)
AB^2 = 9248 - 9248 cos(55°)
Now, we can calculate AB using a calculator:
AB ≈ √(9248 - 9248 cos(55°))
AB ≈ √(9248 - 9248*0.5736)
AB ≈ √(9248 - 5301.5168)
AB ≈ √3946.4832
AB ≈ 62.79
Therefore, the measure of side AB is approximately 62.79.
For a triangle ABC, find the measure of AB given m 55° 55°
55
°
55\degree , m 44° 44°
44
°
44\degree , and side b=68. Hint: this is not a right triangle so you will need to use either the law of sines or the law of cosines to solve it. These formulas are on your Geometry Reference Sheet.
1 answer