In triangle ABC, a line parallel to side BC intersects the height AH at point K and side AC

| September 21, 2021 | education

In triangle ABC, a line parallel to side BC intersects the height AH at point K and side AC at point M. find the sine of angle C if MK = 16, CH = 20 MC = 5.

Since the segment KM, by condition, is parallel to the base of the BC, and the segment AH is the height of the triangle, then the right-angled triangles AKM and AНС are similar in acute angle C.

Let the length of the side АМ be equal to X cm, then the length of the side АС will be equal to (X + 5) cm.

Then the ratio of the sides of similar triangles.

KM / CH = AM / AC.

16/20 = X / (X + 5).

20 * X = 16 * X + 80.

4 * X = 80.

X = AM = 20 cm.

Then AC = 20 + 5 = 25 cm.

In a right-angled triangle ACН, we define the cosine of the ACN angle.

CosACH = CH / AC = 20/25 = 4/5.

Then SihACH = √ (1 – 16/25) = √ (9/25) = 3/5 = 0.6.

Answer: The sine of angle C is 0.6.



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