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MATH / Altitudes (AX)¯ and (BY)¯ of acute triangle ABC intersect at H. If ∠BAC=43^(∘) and ∠ABC=67^(∘), then what is ∠HCA?

Problem

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problem

Altitudes AX¯\overline{AX} and BY¯\overline{BY} of acute triangle ABCABC intersect at HH. If ∠BAC=43∘\angle BAC = 43^\circ and ∠ABC=67∘\angle ABC = 67^\circ, then what is ∠HCA\angle HCA?
Plain-text mathematical notation (without MathML)
Altitudes (AX)¯ and (BY)¯ of acute triangle ABC intersect at H.  If ∠BAC=43^(∘) and ∠ABC=67^(∘), then what is ∠HCA?
Original LaTeX notation
Altitudes $\overline{AX}$ and $\overline{BY}$ of acute triangle $ABC$ intersect at $H$.  If $\angle BAC = 43^\circ$ and $\angle ABC = 67^\circ$, then what is $\angle HCA$?

level

Level 5

type

Geometry

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Source and history

task_id
c6a189ac-5287-509c-b99a-76f1f89d9772
task_key
geometry--test--c6a189ac-5287-509c-b99a-76f1f89d9772
task_revision_id
1
config / split
geometry / test

Official source

initial import