Question

Help!!

The figure shows the dimensions of a sail for a model boat. What is the area of this sail?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Image Attached

Answer 1

21.4 cm²

Proof:

Answer 2

First, we are going to use the law of cosines to find the unknown side of our triangle. Remember that the law of cosines formula is:
`c= \sqrt{a^(2)+b^(2)-2abCosC}`
For the image we can infer that
`a=7`,
`b=8`, and
`C=50`. So lets replace those values in our formula:

`c= \sqrt{7^(2)+8^(2)-2(7)(8)Cos50}`

`c=6.4`

Now that we have all of the sides of our triangle, we are going to use the semi-perimeter formula to find its semi-perimeter:

`s= (a+b+c)/(2)`

`s= (7+8+6.4)/(2)`

`s= (21.4)/(2)`

`s=10.7`

Finally, now that we have the semi-perimeter of our triangle, we can use Heron's formula to find its area:

`A= √(s(s-a)(s-b)(s-c))`

`A= √(10.7(10.7-7)(10.7-8)(10.7-6.4))`

`A= √(10.7(3.7)(2.8)(4.3))`

`A= √(476.6636)`

`A=21.8`

We can conclude that the area of the sail of our boat is 21.8
`cm^2`.