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Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AC=20 and DC=6, what is the length of BC? (Note: the figure is not drawn to scale.)

 
 Aug 5, 2022
 #1
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A

 

        14

                         20

               D         

                  6

B                   C

 

 

Since BD is an altitude....angles BDA  and BDC are right angles......so triangles BDA and BDC are right triangles

 

BD^2 = AB^2  - 14^2   ( 1)

 

BD^2  = BC^2 - 6^2   (2)          subtract (1)  from (2)

 

BC^2  - AB^2  = 14^2  - 6^2

 

BC^2  - AB^2  =  160

 

AB^2  = BC^2  - 160

 

 

So....by the Pythagorean Theorem

 

AB^2  +  BC^2 =  AC^2

 

(BC^2  - 160)  + BC^2 =  20^2

 

2BC^2  - 160  =  400

 

2BC^2  =  560

 

BC^2 =  280

 

BC =  sqrt (280) =   2sqrt (70) ≈  16.733

 

cool cool cool

 
 Aug 5, 2022

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