Question

14 Type the correct answer in the box. A printer creates a right triangular card where the hypoterluse, h, Is three times as long as the shorter leg. What is the length of the longer leg. I, In terms of h? Write the answer In simplest form by replacing a, b, and c with the correct values. (0) OO sin tan cos tan sin-'cos + ΖΔ - а B 9 E 0 2 1 1 כ C A 2 X P 2 1 1 0 ya 4 < > CSC seccot log log, In IA AL abh /= С

Answer 1

Given that a printer creates a right triangular card where the hypotenuse, h, Is three times as long as the shorter leg. We are asked to find the length of the longer leg. This can be seen below.

Step-by-step explanation

Let the of the shorter leg be h. This implies that the length of the hypotenuse is

`\text{Hypotenuse = 3 x h =3h}`

Also, let the longer leg be l. Recall the Pythagoras theorem below;

`\text{Hypotenuse}^2=(Longer\text{ leg)}^2+(\text{Shorter leg)}^2`

We can then insert the assumed parameters into the above

`\begin{gathered} l^2+h^2=(3h)^2 \\ l^2+h^2=9h^2^{} \\ l^2=9h^2-h^2 \\ l^2=8h^2 \\ l=\sqrt[]{8h^2} \\ l=2\sqrt[]{2}h \end{gathered}`

Therefore, by comparison

Answer:

`a=2;b=2;c=1`