In triangle ABC, angle A is 17 degrees, angle B is 23 degrees, CH is height.

| May 4, 2021 | education

In triangle ABC, angle A is 17 degrees, angle B is 23 degrees, CH is height. Find the difference between the angles ACH and BCH.

1. Since the height CH is drawn in triangle ABC (the height of the triangle drawn from the vertex is the perpendicular dropped from this vertex to the opposite side), therefore, we have two triangles – AHC, BHC.
In triangle AHC, angle A = 17 °, angle H = 90 ° (height – perpendicular form a right angle), therefore angle ACH = C = 73 ° (180 – 90 – 17 = 73 °).

In triangle BCH, angle BCH = 67 ° (180 – 90 – 23 = 67 °).

Angle difference ACH – BCH = 73 – 67 = 6 °.

2. Since the height CH is drawn in triangle ABC (the height of the triangle drawn from the vertex is the perpendicular dropped from this vertex to the opposite side), therefore, we have two triangles – AHC, BHC.
In triangle AHC, angle A = 20 °, angle H = 90 ° (height – perpendicular form a right angle), therefore angle ACH = C = 70 ° (180 – 90 – 20 = 70 °).

In triangle BCH, angle BCH = 54 ° (180 – 90 – 36 = 54 °).

Angle difference ACH – BCH = 70 – 54 = 16 °.



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