+834 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?
+1894 First, let's note somethings.
Notice that right triangles ABC, ABE, ABD, BHD, BEC are 30-60-90 triangles.
Right triangles ABe and ADC are 45-45-90 triangles.
Now, let's draw the altitude for triangle ABC by connecting point C to line segment AB.
This line intersects point H on the way.
We know that BAC is is 60 degrees, so that leaves HCA would be 30 degrees.
So 30 degrees is our answer!
Thanks! :)
+1894 First, let's note somethings.
Notice that right triangles ABC, ABE, ABD, BHD, BEC are 30-60-90 triangles.
Right triangles ABe and ADC are 45-45-90 triangles.
Now, let's draw the altitude for triangle ABC by connecting point C to line segment AB.
This line intersects point H on the way.
We know that BAC is is 60 degrees, so that leaves HCA would be 30 degrees.
So 30 degrees is our answer!
Thanks! :)
