Question

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!

Answer 1

• 9 cm

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