Answer :
The missing length of segment TU is [tex]26[/tex] inches. Therefore, the correct answer is option A: [tex]26.7[/tex] inches.
To find the missing length of segment TU, we can use the Pythagorean theorem because it's a right triangle.
Let's denote the lengths as follows:
Length of segment TU:
x (the missing length)
Length of segment TV: [tex]24[/tex] inches
Length of segment UV: [tex]10[/tex] inches
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
So, we have:
[tex]x^{2} =24^{2} +102\\x^{2} =576+100\\x^{2} =676[/tex]
Taking the square root of both sides:
[tex]x=\sqrt{676} \\x=26[/tex]
So, the missing length of segment TU is [tex]26[/tex] inches. Therefore, the correct answer is option A: [tex]26.7[/tex] inches.
COMPLETE QUESTION:
Use the triangles below to find the missing length of segment TU.
A. [tex]26.7[/tex] inches
B. [tex]34[/tex] inches
C. [tex]16[/tex] inches
D. [tex]22[/tex] inches
