Can someone explain how to use trig and solve this? "In triangle ABC, ∠ABC = 90◦...."

[Ilikebugs]

Can someone explain how to use trig and solve this? "In triangle ABC, ∠ABC = 90◦...."

In triangle ABC, ∠ABC = 90◦. A median is drawn from A meeting BC at M suchthat AM = 5. A second median is drawn from C meeting AB at N such thatCN = 2√10.Determine the length of the longest side of triangle ABC

 

[Deleted member 4993]

In triangle ABC, ∠ABC = 90◦. A median is drawn from A meeting BC at M suchthat AM = 5. A second median is drawn from C meeting AB at N such thatCN = 2√10.Determine the length of the longest side of triangle ABC

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[Otis]

Can someone explain how to use trig [to] solve this?

With right triangles, it's standard to label the hypotenuse as side c; the author of this exercise chose to label the hypotenuse as side b, instead, so be aware of that. Draw a diagram.

Were you specifically instructed to use trigonometry, to solve this exercise?

I'm thinking of a method that uses two theorems from geometry (Pythagorean and Apollonius'), to create an easy system of equations to solve for sides a,b,c. (Apollonius related the length of each median to the triangle's three side lengths.)

But, if you need a trigonometric solution, there are other strategies. Realize that triangles NBC and MBA are right triangles. Segments BN and AN are equal. Segments BM and CM are equal. Angles ACN and BCN are equal. Angles BAM and CAM are equal.

Now, we'll wait to see what you've started.