Question

express \\(\cos t\\) as a fraction in simplest terms.

Explanation:

Step1: Find side length TS

Use Pythagorean theorem: $TS = \sqrt{TR^2 - SR^2}$
$TS = \sqrt{25^2 - 24^2} = \sqrt{625 - 576} = \sqrt{49} = 7$

Step2: Apply cosine definition for $\angle T$

Cosine = adjacent/hypotenuse
$\cos T = \frac{TS}{TR}$

Step3: Substitute values and simplify

$\cos T = \frac{7}{25}$

Answer:

$\cos T = \frac{7}{25}$