The side of the rhombus is equal to 2√2 height 2 cm a) Find the acute angle of the rhombus

univerkov | April 8, 2021 | education

The side of the rhombus is equal to 2√2 height 2 cm a) Find the acute angle of the rhombus b) the lengths of the segments into which the height divides the side.

Since the ВН is the height lowered to the AD side, the ABН triangle is rectangular.

Then CosВAН = ВН / AB = 2/2 * √2 = 1 / √2 = √2 / 2.

Angle ВAН = 45.

Let us determine the length of the segment AH.

Since in a right-angled triangle ABН, one of the angles is 45, then triangle ABН is isosceles, which means AH = BH = 2 cm.

Since the sides of the rhombus are equal, the length of the segment НD = АD – АН = 2 * √2 – 2 = 2 * (1 – √2).

Answer: The acute angle of the rhombus is 45. The lengths of the segments into which we divide the side height are equal to 2 cm and 2 * (1 – √2) cm.

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