Answer:
5. x = 30.0
6. x = 8.1
Step-by-step explanation:
For the 25-deg angle, x is the adjacent leg, and 14 is the opposite leg.
The trig ratio that relates the opposite leg to the adjacent leg is the tangent.
[tex] \tan A = \dfrac{opp}{adj} [/tex]
[tex] \tan 25^\circ = \dfrac{14}{x} [/tex]
[tex] x \tan 25^\circ = x [/tex]
[tex] x = \dfrac{14}{\tan 25^\circ} [/tex]
[tex] x = 30.0 [/tex]
6.
For the 36-deg angle, x is the adjacent leg, and 10 is the hypotenuse.
The trig ratio that relates the adjacent leg to the hypotenuse is the cosine.
[tex] \cos A = \dfrac{adj}{hyp} [/tex]
[tex] \cos 36^\circ = \dfrac{x}{10} [/tex]
[tex] 10 \cos 36^\circ = x [/tex]
[tex] x = 10 \cos 36^\circ} [/tex]
[tex] x = 8.1 [/tex]
