Given:
There is a ratio given as 16:9 of width to height and diagonal is 27 iniches
Required:
We need to find the value of height
Explanation:
By ratio
![\begin{gathered} \frac{w}{h}=\frac{16}{9} \\ \\ h=\frac{9}{16}w \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7Bw%7D%7Bh%7D%3D%5Cfrac%7B16%7D%7B9%7D%20%5C%5C%20%20%5C%5C%20h%3D%5Cfrac%7B9%7D%7B16%7Dw%20%5Cend%7Bgathered%7D)
where w is width and h is height
by using pythagorean theorem
![\begin{gathered} 27^2=h^2+w^2 \\ 729=\frac{81}{256}w^2+w^2 \\ \\ 186624=81w^2+256w^2 \\ w^2=553.78 \\ w=23.5\text{ in} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%2027%5E2%3Dh%5E2%2Bw%5E2%20%5C%5C%20729%3D%5Cfrac%7B81%7D%7B256%7Dw%5E2%2Bw%5E2%20%5C%5C%20%20%5C%5C%20186624%3D81w%5E2%2B256w%5E2%20%5C%5C%20w%5E2%3D553.78%20%5C%5C%20w%3D23.5%5Ctext%7B%20in%7D%20%5Cend%7Bgathered%7D)
to find h
![h=\frac{9}{16}*23.5=13.24\text{ in}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B9%7D%7B16%7D%2A23.5%3D13.24%5Ctext%7B%20in%7D)
Final answer:
height is 13.24 inches
$471.90
30 x 15.60 = 468 (total full hours x amount per hour)
60 / 15 = 1/4 (60 minutes per hour divided by the 15 minutes they worked = amount of the hour)
15.60 x 1/4 = 3.9 (amount for the 15 minutes worked)
468 + 3.9 = 471.9 (total full hours + 15 minutes total)
To find the circumference use this formula
C=2πr