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?

Akhain1 Apr 21, 2024

#1**+3 **

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

hasAquestion Apr 21, 2024

#1**+3 **

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

hasAquestion Apr 21, 2024