mimamguliyev
mimamguliyev mimamguliyev
  • 25-01-2022
  • Mathematics
contestada

The perimeter of the rhombus is 40 cm and the cosine of the acute angle is √19 / 10. Find the height of the rhombus

50 points!

Respuesta :

mhanifa
mhanifa mhanifa
  • 25-01-2022

Answer:

  • 9 cm

Step-by-step explanation:

The acute angle is opposite to the height.

Let the height be h and the acute angle α.

Sides of the rhombus are equal, so each side will measure:

  • P / 4 = 40/4 = 10 cm

The ratio of height to hypotenuse is sine:

  • sin α = h / 10

Work out the value of h:

  • h =
  • 10 sin α =
  • 10 √(1 - cos² α) =
  • 10 √(1 - 19/100) =
  • 10 √(81/100) =
  • 10 (9/10) =
  • 9 cm
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