Question

find the exact value of sec y in simplest form. triangle wxy (right - angled at x) has xw = √39, xy = 5, and wy = 8.

Explanation:

Step1: Recall the definition of secant

The secant of an angle in a right triangle is the reciprocal of the cosine of that angle. For angle \( Y \) in right triangle \( XYW \), \(\sec Y=\frac{1}{\cos Y}\), and \(\cos Y = \frac{\text{adjacent side to } Y}{\text{hypotenuse}}\).

Step2: Identify the sides relative to angle \( Y \)

In right triangle \( XYW \) with right angle at \( X \), the side adjacent to angle \( Y \) is \( XY = 5 \), and the hypotenuse is \( WY = 8 \).

Step3: Calculate \(\cos Y\)

Using the definition of cosine, \(\cos Y=\frac{XY}{WY}=\frac{5}{8}\).

Step4: Calculate \(\sec Y\)

Since \(\sec Y=\frac{1}{\cos Y}\), substitute \(\cos Y = \frac{5}{8}\) into the formula: \(\sec Y=\frac{1}{\frac{5}{8}}=\frac{8}{5}\).

Answer:

\(\frac{8}{5}\)