A geometry problem by A Former Brilliant Member

Geometry Level 4

In triangle $ABC$ , $AB = 17$ , $AC=25$ and $AM = \sqrt{261}$ , where $M$ is the midpoint of $BC$ . Find $32 \tan B$ .

1 solution

Maria Kozlowska
Dec 4, 2016

Using Apllonius theorem we get $BM=14$ .

Using cosine rule for triangle $AMB$ we get $cos(B)=\frac{8}{17} \Rightarrow sin(B)=\frac{15}{17} \Rightarrow tan(B)=\frac{15}{8}$ .

Correct solution

A Former Brilliant Member - 4 years, 6 months ago

Did the same way. Only showed calculations in detail.(not necessary since Apllonius theorem is quoted.)

Niranjan Khanderia - 4 years, 6 months ago