Question

A parallelogram is drawn with a 60° angle and its two bases are 5 and 7. What is the height of the parallelogram?

Answer 1

5 * gHeight of the parallelogram is `color(purple)(4.33)` units

Explanation:

Area of parallelogram `A_p = a b sin theta`

Given `a = 7, b = 5, theta = 60^@`

`A_p = 7 * 5 * sin (60) = 7 * 5 * sqrt3/2 = color(purple)(30.31`

`A_p = a * h`

`h = A_p / a = ((35 * sqrt3) /2) / 7 = (5/2)sqrt3 = 4.33` units

Alternatively,

`A_p = a b sin theta = a h`

`:. h = b sin theta = 5 sin (60) = (5*sqrt3)/2 = 4.33` units

Answer 2

h=4.330127019

Explanation:

Using trigonometry, if I make a right angled triangle with the length 5 as the hypotenuse and use the `60^@` to find the height of the triangle. This would be the height of the parallelogram.

sin`60^@=h/5`

`h=5sin60^@`

h=4.330127019