The height of the rhombus divides its sides in half. Find the smallest angle of the rhombus

univerkov | January 10, 2021 | education

Since all sides of a rhombus are equal AB = BC = СD = AD, and according to the condition, the height of the ВН divides the side of the СD in half, DН = CH =СD / 2, then in a right-angled triangle СВН the leg CH is equal to half the length of the hypotenuse BC. СН = ВС / 2, then the angle against the leg СН is 30. Then the angle ВСН = 180 – 90 – 30 = 60.
The acute angle of the rhombus is 60.
Answer: The smallest angle of the rhombus is 60.

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