Answer:
AM = 25, AC = 15, CM = 20
Step-by-step explanation:
The given parameters are;
In ΔACM, ∠C = 90°,  ⊥
 ⊥  , AP = 9, and PM = 16
, AP = 9, and PM = 16
 ² +
² +  ² =
² =  ²
²
 =
 =  + PM = 9 + 16 = 25
 + PM = 9 + 16 = 25
 = 25
 = 25
 ² =
² =  ² +
² +  ² = 9² +
² = 9² +   ²
²
∴  ² = 9² +
² = 9² +   ²
²
Similarly we get;
 ² = 16² +
² = 16² +  ²
²
Therefore, we get;
 ² +
² +  ² = 9² +
² = 9² +   ² + 16² +
² + 16² +  ² =
² =  ² = 25²
² = 25²
2· ² = 25² - (9² + 16²) = 288
² = 25² - (9² + 16²) = 288
 ² = 288/2 = 144
² = 288/2 = 144
 = √144 = 12
 = √144 = 12
From  ² = 9² +
² = 9² +   ², we get
², we get
 = √(9² +  12²) = 15
 = √(9² +  12²) = 15
 = 15
 = 15
From,  ² = 16² +
² = 16² +  ², we get;
², we get;
 = √(16² + 12²) = 20
 = √(16² + 12²) = 20
 = 20.
 = 20.