SOLUTION: In ΔABC, m∠CAB = 60° and AD is an angle bisector with D ∈ BC and AD = 8 ft. Find the distances from D to the sides of the triangle.
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-> SOLUTION: In ΔABC, m∠CAB = 60° and AD is an angle bisector with D ∈ BC and AD = 8 ft. Find the distances from D to the sides of the triangle.
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Question 1106574: In ΔABC, m∠CAB = 60° and AD is an angle bisector with D ∈ BC and AD = 8 ft. Find the distances from D to the sides of the triangle. Answer by greenestamps(13208) (Show Source):
(1) Angle CAB is 60 degrees, and AD bisects it, so angles CAD and BAD are each 30 degrees.
(2) Let E be the point on AB for which DE is perpendicular to AB. Then triangle ADE is a 30-60-90 right triangle with hypotenuse 8; the short leg DE has length 4. But since DE is perpendicular to AB, that is the distance of D from side AB.
The distance of point D from sides AB and AC is 4.
