Question

use the figure to the right to find the length of \\( \overline { t k } \\).
the length of \\( \overline { t k } \\) is \\( \square \\) units. (type an integer or a decimal.)

Explanation:

Step1: Apply the Pythagorean theorem

Since \(TS = 29\) and \(TD=18\), and \(TK\) is calculated using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). Here, \(TK=\sqrt{TS^{2}-TD^{2}}\) (because of the properties of angle - bisector and perpendicular distances, \(TK = TL\) and by Pythagoras in right - triangle \(TLS\) where \(TS\) is the hypotenuse and \(TD\) and \(TK\) are the legs).

$$TK=\sqrt{29^{2}-18^{2}}$$

Step2: Calculate the squares

$$29^{2}=841$$

$$18^{2}=324$$

Step3: Subtract and find the square - root

$$TK=\sqrt{841 - 324}=\sqrt{517}\approx22.7$$

Answer:

\(22.7\)