Question

express cos u as a fraction in simplest terms.

triangle with right angle at t, ut = 10, us = 15, vertices u, t, s

answer attempt 1 out of 2

cos u = blank submit answer

Explanation:

Step1: Recall cosine definition

In a right triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\) for an angle \(\theta\).

Step2: Identify sides for \(\angle U\)

In \(\triangle TUS\) (right - angled at \(T\)), for \(\angle U\):

• Adjacent side to \(\angle U\) is \(UT = 10\)
• Hypotenuse is \(US=15\)

Step3: Calculate \(\cos U\)

Using the cosine formula \(\cos U=\frac{\text{adjacent to }U}{\text{hypotenuse}}=\frac{UT}{US}\)
Substitute \(UT = 10\) and \(US = 15\) into the formula: \(\cos U=\frac{10}{15}=\frac{2}{3}\) (simplify the fraction by dividing numerator and denominator by 5)

Answer:

\(\frac{2}{3}\)