Question

A brace for a shelf has the shape of a right triangle. Its hypotense is 16 incges long and the two legs are equal in length. How long arr the legs of the triangle

Answer 1

We use trigonometry because we know an angle and a side length. 

We are looking for one of the sides that isn't the hypotenuse:
As illustrated by the picture I made below:

We know both unknown angles will be 45 degrees, as there are 180 degrees in a triangle, we know the triangle is a right angle triangle (has 90 degrees) so, (180-90)/2 = 45

Using SOH CAH TOA, short for :  SIN- OH  COS- AH  TAN- OA

We are looking for the one with H, as we know what H is.
I am picking "SIN- OH", but we could use "COS- AH"

The formula for this is: Sin(angle) = O/H
We substitute the angle (45) and the length for H (16)

Sin(45)= O/16 <- rearrange it
Sin(45)*16= O <- Solve in the calculator
13.6145 (4 DP)= O
The legs = O

The legs have a length of "13.6145 (4 DP)" each