El producto escalar o producto punto entre dos vectores \( \vec{u} \) y \( \vec{v} \) se define como \( \vec{u} \cdot \vec{v}=|\vec{u}||\vec{v}| \cos \theta \), donde \( \theta \) es el ángulo entre ambos vectores. Si \( \vec{u} \) es ortogonal a \( \vec{v} \), entonces sobre el ángulo \( \theta \) es ciertc que

In \( \triangle \mathrm{TUV}, u=750 \mathrm{~cm}, m \angle \mathrm{~T}=105^{\circ} \) and \( m \angle \mathrm{U}=42^{\circ} \). Find the length of \( t \), to the nearest centimeter.

In \( \triangle \mathrm{FGH}, f=7.4 \) inches, \( g=1 \) inches and \( h=7 \) inches. Find the measure of \( \angle \mathrm{G} \) to the nearest degree.

In \( \triangle X Y Z, x=410 \) inches, \( y=450 \) inches and \( z=210 \) inches. Find the measure of \( \angle X \) to the nearest degree.

(c) \( \sin (\pi+x)+\cos \left(\frac{\pi}{2}-x\right)+\tan \left(\frac{\pi}{2}+x\right)+\tan \left(\frac{3 \pi}{2}-x\right) \)

In \( \triangle \mathrm{PQR}, p=4.7 \) inches, \( m \angle \mathrm{P}=76^{\circ} \) and \( m \angle \mathrm{Q}=57^{\circ} \). Find the length of \( q \), to the nearest 10th of an inch.