In triangle ABC, angle C is 90 degrees, height CH is 24, BH = 7. Find sinA.

In triangle ABC:

Angle C is 90 °;
Height CH = 24;
BH = 7.
Find sin A.

Decision:

1) Consider a triangle BCH, where the angle H = 90 °.

Let’s find the aircraft.

ВС = √ (CH ^ 2 + BH ^ 2) = √ (24 ^ 2 + 7 ^ 2) = √ (576 + 49) = √625 = √25 ^ 2 = 25;

2) Since sin a = cos b in triangle ABC, then we find cos b in triangle BCH.

cos b = ratio of the adjacent HL leg to the HV hypotenuse.

We get the formula in the form:

cos b = BH / BC;

cos b = 7/25;

Since, sin a = cos b, then sin a = 7/25;

Answer: sin a = 7/25.