Answer/Step-by-step explanation:
Apply trigonometric ratio to solve for x in all problems given.
1. Reference angle = 29°
Adjacent = x
Hypotenuse = 13 m
Thus:
[tex] cos(29) = \frac{x}{13} [/tex]
Multiply both sides by 13
[tex] 13*cos(29) = x [/tex]
11.4 = x (nearest tenth)
x = 11.4 m
2. Reference angle = 63°
Opp = 18 cm
Hypotenuse = x
Thus:
[tex] sin(63) = \frac{18}{x} [/tex]
Multiply both sides by x
[tex] x*sin(63) = 18 [/tex]
Divide both sides by sin(63)
[tex] x = \frac{18}{sin(63)} [/tex]
x = 20.2 cm (nearest tenth)
3. Reference angle = 71°
Opp = 14 ft
Adjacent = x
Thus:
[tex] tan(71) = \frac{14}{x} [/tex]
Multiply both sides by x
[tex] x*tan(71) = 14 [/tex]
Divide both sides by tan(71)
[tex] x = \frac{14}{tan(71)} [/tex]
x = 4.8 ft (nearest tenth)
