Question

In triangle ABC, AC = 15, BC = 11, and m∠C = 75. To the nearest tenth, what is the length of AB¯¯¯¯¯¯ ?

Answer 1

Answer:
AB = 16.14279 units

Explanation:
To solve this question, we will use the cosine rules shown in the attached image.
We are given that:
a = BC = 11
b = AC = 15
c = AB that we want to calculate
measure angle C = 75 degrees

We will substitute in the third rule to get the value of c as follows:
c^2 = a^2 + b^2 - 2ab*cos(C)
c^2 = (11)^2 + (15)^2 - 2(11)(15)cos(75)
c^2 = 260.589
c = 16.14279 units
Therefore:
AB = 16.14279 units

Hope this helps :)