Question

In a triangle abc. Ab=5 ac= 6. Bc=8 find the length of median ad

Answer 1

Answer=3cm
Reason=as we have to find length of ad and d is mid point of line BC. then there would be another triangle that is abd two sides of abd are 4 and 5 then its third side will be 3 according Pythagorean triplet.

Answer 2

Answer:

3.8

Step-by-step explanation:

Given: A triangle ABC, AB = 5, AC = 6, BC = 8

Let length of median AD be x

Formula used: Cosine law

$\cos B=\dfrac{a^2+c^2-b^2}{2ac}$

In ΔABC, AB=c=5 , AC=b=6, BC=a=8

Substitute into formula and find angle B

$\cos B=\dfrac{8^2+5^2-6^2}{2\cdot 8\cdot 5}$

$\cos B=0.6625$

$\angle B=\cos^{-1}(0.6625)$

$\angle B=48.5^\circ$

In ΔABD, AB=c=5 , AD=b=x, BD=a=4

BD is half of AB (because D is mid point of AB)

Substitute into formula and find angle B

$\cos B=\dfrac{4^2+5^2-x^2}{2\cdot 4\cdot 5}$

$0.6625=\dfrac{41-x^2}{40}$

$x^2=41-40\cdot 0.6625$

$x=\sqrt{14.5}$

$x=3.8$

Hence, The length of median AD is 3.8