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Altitudes AD and BE of acute triangle ABC intersect at point H. If angle ABH = 30 and angle DAC = 45, then what is angle HCA in degrees?

 

 Apr 21, 2024

Best Answer 

 #1
avatar+45 
+1

Well we have right triangles ADC, ABD, ABE, BEC, BHD

 

triangle ABE is a 30-60-90 and ADC is a 45-45-90

 

and then im stuck, :( 

 

 

 

some things i did notice were AHE and BHD are 45-45-90 triangles, and since ABE is a 30-60-90 triangle, BAH is 15 degrees,

 

...

 

i think i got it

 

make the altitude for triangle on ABC on segment AB, and since BAC is 60 degrees, HCA would be 30 degrees

 

 

cheekylaughwink

 Apr 21, 2024
edited by hasAquestion  Apr 21, 2024
 #1
avatar+45 
+1
Best Answer

Well we have right triangles ADC, ABD, ABE, BEC, BHD

 

triangle ABE is a 30-60-90 and ADC is a 45-45-90

 

and then im stuck, :( 

 

 

 

some things i did notice were AHE and BHD are 45-45-90 triangles, and since ABE is a 30-60-90 triangle, BAH is 15 degrees,

 

...

 

i think i got it

 

make the altitude for triangle on ABC on segment AB, and since BAC is 60 degrees, HCA would be 30 degrees

 

 

cheekylaughwink

hasAquestion Apr 21, 2024
edited by hasAquestion  Apr 21, 2024

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