Question

express cos w as a fraction in simplest terms.
(image of a right triangle wxy with right angle at x, xy = 18, wy = 30)
answer attempt 1 out of 2
cos w = | input box | submit answer

Explanation:

Step1: Identify triangle type

Triangle \( WXY \) is right - angled at \( X \), so it's a right triangle. We know the length of hypotenuse \( WY = 30\) and one leg \( XY = 18\). Wait, no, in a right triangle, for angle \( W \), the adjacent side and opposite side need to be identified. First, we can find the length of the other leg \( WX \) using the Pythagorean theorem. Let \( WX = a\), \( XY = 18\), \( WY = 30\). By Pythagoras, \( a^{2}+18^{2}=30^{2}\), so \( a^{2}=30^{2}-18^{2}=(30 - 18)(30 + 18)=12\times48 = 576\), so \( a = 24\).

Step2: Recall cosine definition

In a right triangle, \( \cos\theta=\frac{\text{adjacent side to } \theta}{\text{hypotenuse}}\). For angle \( W \), the adjacent side is \( WX = 24\) and the hypotenuse is \( WY = 30\).

Step3: Simplify the fraction

\( \cos W=\frac{24}{30}=\frac{4}{5}\) (dividing numerator and denominator by 6).

Answer:

\(\frac{4}{5}\)