In a right-angled triangle ABC, angle C = 90 degrees M midpoint AC N midpoint CB MN 6 cm angle
July 28, 2021 | education
| In a right-angled triangle ABC, angle C = 90 degrees M midpoint AC N midpoint CB MN 6 cm angle MNC = 60 degrees. Find the sides of triangle ABC. cos B. Area of triangle MNC.
Consider a right-angled triangle ABC with right angle C.
Points M and N are midpoints of legs AC and CB and MN = 6, angle MNC = 60 °.
MN is the midline of triangle ABC. Consequently,
MN = 1/2 * AB and MN is parallel to AB. From this we get
AB = 2 * MN = 2 * 6 = 12 and ABC angle = MNC angle = 60 °.
Then
AC = AB * sin (ABC) = 12 * sin (60 °) = 12 * √3 / 2 = 6 * √3.
BC = AB * cos (ABC) = 12 * cos (60 °) = 12 * 1/2 = 6.
Area S of triangle MNC:
S = 1/2 * CM * CN = 1/2 * AC / 2 * CB / 2 = AC * CB / 8 =
= 6 * 6 * √3 / 8 = 9 * √3 / 2.
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