Answer:
a. 3.5 mm
b. 75.5 in.
c. 78.4 ft
Step-by-step explanation:
a.
x is opposite the 26-deg acute angle.
8 mm is the hypotenuse.
The trigonometric ratio that relates the opposite leg to the hypotenuse is the sine ratio.
[tex] \sin A = \dfrac{opp}{hyp} [/tex]
[tex] \sin 26^\circ = \dfrac{x}{8} [/tex]
[tex] x = 8 \sin 26^\circ [/tex]
[tex] x = 3.506969... [/tex]
[tex] x = 3.5~mm [/tex]
b.
The 40-inch leg is adjacent to the 58-deg acute angle.
x is the hypotenuse.
The trigonometric ratio that relates the adjacent leg to the hypotenuse is the cosine ratio.
[tex] \cos A = \dfrac{adj}{hyp} [/tex]
[tex] \cos 58^\circ = \dfrac{40}{x} [/tex]
[tex] x\cos 58^\circ = 40 [/tex]
[tex] x = \dfrac{40}{\cos 58^\circ} [/tex]
[tex] x = 75.483... [/tex]
[tex] x = 75.5~in. [/tex]
c.
For the 71-deg acute angle, 27 ft is the adjacent leg, and x is the opposite leg. The trigonometric ratio that relates the opposite leg to the adjacent leg is the tangent ratio.
[tex] \tan A = \dfrac{opp}{adj} [/tex]
[tex] \tan 71^\circ = \dfrac{x}{27} [/tex]
[tex] x = 27 \tan 71^\circ [/tex]
[tex] x = 78.4136... [/tex]
[tex] x = 78.4~ft [/tex]
