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The angle between the median CM and the hypotenuse AB of right triangle ABC is equal to 30°. Find the area of ABC if the altitude CH is equal to 4.


I am extremely sorry I tried but didn't make any desired progress that would help in solving the question

Death Champion
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1 Answers1

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Hint: In a right triangle, you have $AB=2CM$. (If you don't know this, try proving it!) Also, $\triangle{CHM}$ is a $30-60-90$ triangle.

Please work on the question on your own before viewing the solution.

Since $CH=4$ and $\angle{CMH}=30^{\circ}$, we have $CM=2CH=8$. We also know that $CM=AM=BM$, so $AM=BM=8$. Thus, your answer is $$\dfrac{1}{2}\cdot AB\cdot CH=\dfrac{1}{2}\cdot(8+8)\cdot 4=\boxed{32}$$

MathMagician
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  • Yeah I got it, that's y came back to give the answer to the question but u also answered it, thanks anyways... I was just strolling in our garden for night walk, and the idea flashed through my mind... – Death Champion Mar 04 '22 at 17:50