Question

what is ut?
ut =
in the triangle, ∠u is a right angle, uv = 8, tv = 17

Explanation:

Step1: Identify right triangle sides

We have right triangle $\triangle TUV$ with right angle at $U$. Hypotenuse $TV=17$, leg $UV=8$, unknown leg $UT$.

Step2: Apply Pythagorean theorem

Pythagorean theorem: $a^2 + b^2 = c^2$, rearranged to $a = \sqrt{c^2 - b^2}$ for $UT$.
$$UT = \sqrt{TV^2 - UV^2}$$

Step3: Substitute values and calculate

$$UT = \sqrt{17^2 - 8^2} = \sqrt{289 - 64} = \sqrt{225}$$

Step4: Simplify square root

$$\sqrt{225} = 15$$

Answer:

15