what would the diagonal bottom if the angles 12 inches 16 inches 35 inches
It appears you are describing a right triangle with sides measuring 12 inches and 16 inches, and it seems you are asking for the length of the diagonal (which would be the hypotenuse in the case of a right triangle).
To find the length of the hypotenuse of a right triangle, we use the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
where:
- \( a \) is the length of one of the shorter sides (one of the legs of the right triangle),
- \( b \) is the length of the other shorter side,
- \( c \) is the length of the hypotenuse.
Given the sides of 12 inches and 16 inches:
\[ (12)^2 + (16)^2 = c^2 \]
\[ 144 + 256 = c^2 \]
\[ 400 = c^2 \]
To find \( c \), you take the square root of 400:
\[ c = \sqrt{400} \]
\[ c = 20 \]
So the length of the diagonal (hypotenuse) is 20 inches.
The 35 inches you mentioned does not fit into this right triangle—it's too long to be the hypotenuse for a right triangle with legs of 12 inches and 16 inches. If you meant to include the 35 inches as one of the sides, then the Pythagorean theorem won't apply because the sides you described won't form a right triangle. In this case, we have a triangle with sides of 12 inches, 16 inches, and 35 inches, which doesn't satisfy the Pythagorean theorem because \(12^2 + 16^2 \neq 35^2\).