Question

. Using ratios and the Pythagorean Theorem the approximate width is 23.5 inches and the height is inches.

Answer 1

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

$\begin{gathered} \frac{w}{h}=\frac{16}{9} \\ \\ h=\frac{9}{16}w \end{gathered}$

where w is width and h is height

by using pythagorean theorem

$\begin{gathered} 27^2=h^2+w^2 \\ 729=\frac{81}{256}w^2+w^2 \\ \\ 186624=81w^2+256w^2 \\ w^2=553.78 \\ w=23.5\text{ in} \end{gathered}$

to find h

$h=\frac{9}{16}*23.5=13.24\text{ in}$

Final answer:

height is 13.24 inches