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In a certain isosceles right triangle, the altitude to the hypotenuse has length $6$. What is the area of the triangle?

 Oct 26, 2019
edited by Guest  Oct 26, 2019
 #1
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Please help me

fast!

 Oct 26, 2019
 #2
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1. Input data entered: angle α, angle β, angle γ and height h
 alpha = 45° ; ; beta = 45° ; ; gamma = 90° ; ; h = 6 ;

 
2. From height h and angle α we calculate side a:
a = { h }/{ sin beta } = { 6 }/{ sin (45° ) } = 8.485 ; ; b = { h }/{ sin alpha } = { 6 }/{ sin (45° ) } = 8.485 ; 


3. From side a and angle α we calculate hypotenuse c:
 sin alpha = a:c ;  c = a/ sin alpha = 8.485/ sin(45 ° ) = 12 ; ; 
Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 8.49 ; ; b = 8.49 ; ; c = 12 ; ; 

4. The triangle area - from two legs
Area = { ab }/{ 2 } = { 8.49 * 8.49 }/{ 2 } = 36 Sq. units. 

 Oct 26, 2019
 #3
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Thank you guest!

CalculatorUser  Oct 26, 2019

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