Define the tangent function using an example from a specific right triangle with known angles and side lengths.

25. यदि लगाउनुहोस् । If \( 9 \cos \theta+40 \sin \theta=41 \), find the value of \( \tan \theta \).

In a right triangle, if one angle measures 30 degrees and the length of the side opposite this angle is 5 units, what is the length of the hypotenuse?

23. El menor valor del ángulo \( x\left(0^{\circ} \leq x<180^{\circ}\right) \) que satisface la ecuación trigonométrica \( \cos ^{2}(x)-3 \cdot \operatorname{sen}^{2}(x)=0 \) es: A. \( 120^{\circ} \) B. \( 30^{\circ} \) C. \( 150^{\circ} \) D. \( 60^{\circ} \)

Soit \( A B C \) un triangle rectangle en B tel que \( : \cos \widehat{B A C}=\frac{3}{4} \) 11 Montrer que \( : \sin \widehat{B A C}=\frac{\sqrt{7}}{4} \) 2 Calculer : \( \tan \widehat{B A C} \) 3 Calculer : \( \sin \widehat{A C B}, \cos \widehat{A C B} \) et \( \tan \widehat{A C B} \) 4 On suppose que: \( A B=5 \mathrm{~cm} \). Calculer \( A C \)

Simplifier: \( B=3 \cos 10^{\circ}+5 \cos ^{2} 15^{\circ}+5 \cos ^{2} 75^{\circ}-3 \sin 80^{\circ} \)