The height of an acute-angled triangle ABC forms angles of 24g and 38g

The height of an acute-angled triangle ABC forms angles of 24g and 38g with the sides extending from the same vertex. Find the angles of the triangle ABC.

Suppose that the height is lowered from the top B to the AC side. Let’s designate it ВН, ∠АВН = 24 °, ∠СВН = 38 °.
∠В = 24 ° + 38 ° = 62 °.
The height ВН divides the ABC triangle into two right-angled triangles. Let’s consider each of them.
In triangle AВН:
∠А = 90 ° – ∠АВН = 90 ° – 24 ° = 66 °.
In the SVN triangle:
∠С = 90 ° – ∠СВН = 90 ° – 38 ° = 52 °.
Verification:
∠А + ∠В + ∠С = 66 ° + 62 ° + 52 ° = 180 °.
Answer: the angles of the triangle are 66 °, 62 °, 52 °.