Median

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

Calculate the length of the median to side b (tb).

Correct answer:

t₂ =  11.66 cm

Step-by-step explanation:

$$\begin{gathered} a=10\text{cm} \\ {t}_1=13\text{cm} \\ \gamma =90{}^{\circ } \\ {b}^2=t_a^2-(a/2{)}^2 \\ b=\sqrt{t_1^2-(a/2{)}^2}=\sqrt{13^2-(10/2{)}^2}=12\text{cm} \\ {t}_2^2=a^2+(b/2{)}^2 \\ {t}_2=\sqrt{a^2+(b/2{)}^2}=\sqrt{10^2+(12/2{)}^2}=2\sqrt{34}=11.66\text{cm} \end{gathered}$$

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