Answer:
Explanation:
Given two segment measures in a right triangle diagram, you want the values of the other measures.
Pythagorean theorem
The Pythagorean theorem can be used to find y:
BC² = BD² +CD²
65² = y² +25²
y² = 65² -25² = 3600
y = √3600 = 60
Similar triangles
The proportionality of corresponding sides in similar triangles can be used to find the remaining measures.
short side/hypotenuse = 25/65 = 65/(25+x)
25 +x = 65²/25 = 169
x = 144
And for z, we can use ...
long side/hypotenuse = AB/AC = BD/BC
z/169 = 60/65
z = 169(12/13) = 156
The triangle measures are ...