Question

express \\(\cos t\\) as a fraction in simplest terms.
triangle image with right angle at s, hypotenuse tr = 25, leg sr = 24
answer attempt 1 out of 2
\\(\cos t = \square\\)

Explanation:

Step1: Recall the cosine formula

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For angle $T$, the adjacent side to angle $T$ is $TS$, and the hypotenuse is $TR = 25$.
First, find the length of $TS$ using the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 25$ (hypotenuse) and $b = 24$ (one leg). Let $a=TS$. Then $TS=\sqrt{TR^{2}-SR^{2}}=\sqrt{25^{2}-24^{2}}=\sqrt{(25 + 24)(25 - 24)}=\sqrt{49}=7$.

Step2: Calculate $\cos T$

Using the cosine formula $\cos T=\frac{TS}{TR}$. Since $TS = 7$ and $TR = 25$.

Answer:

$\frac{7}{25}$