In triangle ABC, angle A is 51 degrees, angle B is 60 degrees .AD, BE and CF are heights intersecting

In triangle ABC, angle A is 51 degrees, angle B is 60 degrees .AD, BE and CF are heights intersecting at point O. find the angle AOF.

1) Triangle ABC.

Angle A = 51 ° and angle B = 60 °.

Find corner C.

Angle С = 180 ° – 51 ° – 60 ° = 120 ° – 51 ° = 50 ° + 20 ° – 1 ° = 50 ° + 19 ° = 69 °.

2) AD, BE and CF are the heights of the ABC triangle.

3) ABE triangle.

Angle ABE = 180 ° – angle BEA – angle BAE = 180 ° – 90 ° – 51 ° = 90 ° – 51 ° = 40 ° – 1 ° = 39 °;

4) Triangle BAD.

Angle WAD = 180 ° – 90 ° – 60 ° = 90 ° – 60 ° = 30 °.

5) Triangle ABO.

Angle A = 30 ° and angle B = 39 °.

BOA angle = 180 ° – 30 ° – 39 ° = 150 ° – 39 ° = 120 ° – 9 ° = 111 °;

6) The AFO triangle.

Angle AOF = 180 ° – 90 ° – 30 ° = 90 ° – 30 ° = 60 °;

Answer: Angle AOF = 60 °.