Question

Стороны параллелограмма равны 10 см и 16 см, а угол между ними 60 градусов. Найдите диагонали параллелограмма.

Answer 1

 АВСD-параллелограмм

АС и ВD-диаганали 

ВD^2=AB^2+AD^2-2AB*AD*cos60

ВD^2=10^2+16^2-2*10*16*0,5

ВD^2=100+256-160

ВD^2=196

BD=14см

BD^2+AC^2=2(AB^2+AD^2)

AC^2=2(AB^2+AD^2)-BD^2

AC^2=2(10^2+16^2)-14^2

AC^2=516

АС=корень из 516

 

Answer 2

Finding the Diagonals of a Parallelogram

To find the diagonals of a parallelogram, we can use the given information about the sides and angle of the parallelogram.

Given: - Sides of the parallelogram: 10 cm and 16 cm - Angle between the sides: 60 degrees

To find the diagonals, we can use the following formulas:

1. Diagonal 1 (d1) can be found using the formula: d1 = √(a^2 + b^2 - 2abcos(θ)) where a and b are the lengths of the sides and θ is the angle between them.

2. Diagonal 2 (d2) can be found using the formula: d2 = √(a^2 + b^2 + 2abcos(θ)) where a and b are the lengths of the sides and θ is the angle between them.

Let's calculate the diagonals using the given information:

1. Diagonal 1 (d1): - Length of side a = 10 cm - Length of side b = 16 cm - Angle θ = 60 degrees

Plugging these values into the formula, we get: d1 = √(10^2 + 16^2 - 2 * 10 * 16 * cos(60))

Calculating this expression, we find that: d1 ≈ 19.36 cm.

2. Diagonal 2 (d2): - Length of side a = 10 cm - Length of side b = 16 cm - Angle θ = 60 degrees

Plugging these values into the formula, we get: d2 = √(10^2 + 16^2 + 2 * 10 * 16 * cos(60))

Calculating this expression, we find that: d2 ≈ 7.36 cm.

Therefore, the diagonals of the parallelogram are approximately 19.36 cm and 7.36 cm in length.