Question

find z.
write your answer as an integer or as a decimal rounded to the nearest tenth.
z =
submit
work it out
not feeling ready yet? these can help:

Explanation:

Step1: Find the measure of angle \( Y \)

In a triangle, the sum of angles is \( 180^{\circ} \). So, \( \angle Y=180^{\circ}-25^{\circ}-50^{\circ}=105^{\circ} \)

Step2: Apply the Law of Sines

The Law of Sines states that \( \frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c} \). Here, \( \frac{\sin X}{YZ}=\frac{\sin Z}{XY} \). Substituting the values: \( \frac{\sin25^{\circ}}{4}=\frac{\sin50^{\circ}}{z} \)

Step3: Solve for \( z \)

Cross - multiply: \( z\times\sin25^{\circ}=4\times\sin50^{\circ} \). Then \( z = \frac{4\times\sin50^{\circ}}{\sin25^{\circ}} \).
We know that \( \sin25^{\circ}\approx0.4226 \) and \( \sin50^{\circ}\approx0.7660 \).
\( z=\frac{4\times0.7660}{0.4226}=\frac{3.064}{0.4226}\approx7.2 \)

Answer:

\( z = 7.2 \)