Mr. Alvarez wants to make a gate that is three
feet wide and five feet high. He needs to cut a
board to nail across the diagonal of the gate.
How long a board does he need?

Mr. Alvarez needs a board of length 5.83 feet

Step-by-step explanation:

Step 1 :

Given

Width of the gate = 3 feet

Height of the gate = 5 feet

We need to find the board's length to fix across the diagonal of the gate

Step 2 :

The gate is in the shape of a rectangle with sides 3 and 5 feet. So we need to find this rectangle's diagonal . Let l be the diagonal's length

Using Pythagoras theorem,

l² = 5² + 3²  = 25 + 9 = 34

=> l = √34  = 5.83 feet

Step 3 :

Answer :

Mr. Alvarez needs a board of length 5.83 feet

r and t.

both are 64 degrees.