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# help geometry

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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

#1
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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

Apr 21, 2024
edited by hasAquestion  Apr 21, 2024

#1
+60
+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
edited by hasAquestion  Apr 21, 2024