Question

The sides of a parallelogram are 40 feet and 70 feet long, and the smaller angle has a measure of 36°. find the length of the longer diagonal to the nearest whole number. 44 ft 64 ft 69 ft 105 ft

Answer 1

105 ft

Explanation:

Answer 2

1. Identify the parallelogram as
`ABCD`.

2. The diagonal divides it into two congruent triangles, so let's take only the triangle
`ABD`, where
`BD` is the diagonal.

3. Now, you must apply the Law of Cosines:

`c=\sqrt{a^(2)+b^(2)-2abCos(C)}`

Where
`a=40ft; b=70 ft` and
`C` is the angle between
`A` and
`B`.

4.
`C` and
`36 degrees` are suplementary. Therefore:

`C=180degrees-36degrees=144degrees`

5. Substitute values into the formula:

`c=\sqrt{40^(2)+70^(2)-2(40)(70)Cos(144)} =105ft`

The answer is:
`105ft`