Final answer:
The acute angle formed by the altitudes from point A to side BC and from point B to side AC in triangle ABC can be found using the properties of triangles. Angle X is 50° and angle Y is 30°.
Step-by-step explanation:
The acute angle formed by the altitudes from A to BC and from B to AC can be found using the properties of triangles. First, let's denote the acute angle formed by the altitude from A to BC as angle X and the acute angle formed by the altitude from B to AC as angle Y.
We know that angle B is 40° and angle C is 60°. Since the sum of the angles in a triangle is 180°, angle A can be calculated as 180° - 40° - 60° = 80°. Now, we have a triangle ABC with angle A as 80°, angle B as 40°, and angle C as 60°.
Since we are looking for the acute angles formed by the altitudes, we need to find the acute angle formed by the altitude from A to BC, which is angle X. Angle X is equal to the complementary angle of angle B. Therefore, angle X is 90° - 40° = 50°. Similarly, angle Y is the complementary angle of angle C, so angle Y is 90° - 60° = 30°. Therefore, the acute angle formed by the altitude from A to BC is 50°, and the acute angle formed by the altitude from B to AC is 30°.