A straight line is drawn through point K on the side AB of a right-angled triangle
| September 1, 2021 | education
A straight line is drawn through point K on the side AB of a right-angled triangle, perpendicular to the hypotenuse BC and intersect at point M. Find BC if AC = 20 cm, KM = 8 cm, KB = 10 cm.
Consider the triangle KMB.
Since the angle (KMB) is straight, then:
KB = KM * sin (B)
sin (B) = KM / KB
sin (B) = 8/10
sin (B) = 4/5
Consider a triangle ABC.
Since the angle (BAC) is straight, then:
BC * sin (B) = AC
BC = AC / sin (B)
BC = 20 * 5/4
BC = 25 cm.
Answer: 25 cm.
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