# Median

In triangle ABC is given side a=10 cm and median ta= 13 cm and angle gamma 90°.

Calculate length of the median tb.

Result

tb =  11.66 cm

#### Solution:

$b^2 = t_a^2 -(a/2)^2 \ \\ b = \sqrt{ 13^2 - (10/2)^2 } = 12 \ cm \ \\ \ \\ t_b^2 = a^2 + (b/2)^2 \ \\ t_b = \sqrt{ 10^2 + (12/2)^2 } = 11.66 \ \text{cm}$

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