SOLUTION: (44) Find the altitude of the triangle to side AB. Link to diagram: https://ibb.co/spznGBS7

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Question 1209522: (44) Find the altitude of the triangle to side AB.
Link to diagram: https://ibb.co/spznGBS7

Answer by ikleyn(52747) About Me  (Show Source):
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(44) Find the altitude of the triangle to side AB.
Link to diagram: https://ibb.co/spznGBS7
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Using three given sides of the triangle a, b, c, find its area by the Heron's formula

    area = sqrt%28s%2A%28s-a%29%2A%28s-b%29%2A%28s-c%29%29,


where s = %28a%2Bb%2Bc%29%2F2 = %286%2B7%2B9%29%2F2 = 11 is the semi-perimeter.


So, the area is

    area = sqrt%2811%2A%2811-6%29%2A%2811-7%29%2A%2811-9%29%29 = sqrt%2811%2A5%2A4%2A2%29 = 2%2Asqrt%28110%29.


Another formula for the area of the triangle is

    area = %281%2F2%29%2AAB%2Ah,  

where h is the altitude drawn to the sides AB.


It gives you an equation

    %281%2F2%29%2A6%2Ah = 2%2Asqrt%28110%29 

or

    3*h = 2%2Asqrt%28110%29.


From this equation,  h = %282%2F3%29%2Asqrt%28110%29 = 6.99206  (rounded).    ANSWER

At this point, the problem is solved in full.