# In △XYZ , m∠X=38∘ , m∠Z=67∘ , and YZ=25 feet . What is XZ ? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.

May 24, 2018

$\approx 39.2 \setminus \text{ft}$

#### Explanation:

By the sine law for triangles

$\frac{X Z}{\sin \angle Y} = \frac{Y Z}{\sin \angle X}$

Thus we need to know $\text{m} \angle Y$. This follows easily from

$\text{m"/_X+"m"/_Y+"m} \angle Z = {180}^{\circ}$

and is

$\text{m} \angle Y = {180}^{\circ} - {38}^{\circ} - {67}^{\circ} = {75}^{\circ}$

Thus

$X Z = Y Z \times \frac{\sin \angle Y}{\sin \angle X} = 25 \setminus \text{ft} \times \frac{\sin {75}^{\circ}}{\sin {38}^{\circ}}$

$q \quad \approx 25 \times \frac{0.9659}{0.6157} \setminus \text{ft" ~~39.22\ "ft}$