Question

find xy.
triangle with right angle at z, angle at y is 50 degrees, side yz is 5. prompt: write your answer as an integer or as a decimal rounded to the nearest tenth. xy =

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( XYZ \) with right angle at \( Z \), we know the length of \( YZ = 5 \) and the angle at \( Y \) is \( 50^\circ \). We need to find the length of \( XY \) (the hypotenuse). The cosine of an angle in a right triangle is defined as the adjacent side over the hypotenuse. So, \( \cos(50^\circ)=\frac{YZ}{XY} \).

Step2: Solve for \( XY \)

We can rearrange the formula to solve for \( XY \): \( XY = \frac{YZ}{\cos(50^\circ)} \). We know \( YZ = 5 \) and \( \cos(50^\circ) \approx 0.6428 \). Plugging in the values, we get \( XY=\frac{5}{\cos(50^\circ)}\approx\frac{5}{0.6428}\approx7.8 \).

Answer:

\( 7.8 \)