The blanks are filled and attached
How to determine the sides of the triangle
Information given from the question is interpreted as:
10 = opposite
7 = adjacent
a = hypotenuse
Using Pythagoras theorem given by the the formula
hypotenuse² = opposite² + adjacent²
plugging the values as in the problem
a² = 10² + 7²
a² = 100 + 49
a² = 149
a = √149
a = 12.08
5 = opposite
a = adjacent
c = hypotenuse
plugging the values as in the problem
c² = (√149)² + 5²
c² = 149 + 25
c² = 174
c = √174
c = 13.19