The approximate measures of the remaining side lengths of the triangle are |AC| = 72 units approximately and |BC| = 31 units approximately.
For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,
we have, by law of sines,
[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]
Remember that we took
[tex]\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}[/tex]
Sum of angles in any triangle = 180 degrees
m∠A + m∠B + m∠C = 180 degrees
25 + m∠B + 55 = 180 degrees
m∠B = 180 - 55 - 25 = 100 degrees.
Using sine law, we get:
[tex]\dfrac{sin\angle A}{|BC|} = \dfrac{sin\angle B}{|AC|} = \dfrac{sin\angle C}{|AB|}[/tex]
If we take: |BC| = x units, |AC| = y units, then:
[tex]\dfrac{\sin(25)}{x} = \dfrac{\sin(55)}{60}\\\\\dfrac{\sin(100)}{y} = \dfrac{\sin(55)}{60}[/tex]
(used angle C in both equation so as to leave only one variable in one equation as side opposite to angle C (ie AB) is known, so that will help keep constants more and more.)
Thus, we get:
[tex]|BC| =x = \dfrac{60 \times \sin(25)}{\sin(55)} \approx 31 \: \rm units \\\\|AC| =y = \dfrac{60 \times \sin(100)}{\sin(55)} \approx 72 \: \rm units\\[/tex]
Thus, the approximate measures of the remaining side lengths of the triangle are |AC| = 72 units approximately and |BC| = 31 units approximately.
Learn more about law of sines here:
https://brainly.com/question/17289163
