Answer:
x = 74.3
Step-by-step explanation:
Using the trigonometric ratio formula, the missing side, x, of the right angled triangle, can be found as follows:
Ѳ = 22°,
adjacent side length = x
Opposite side length = 30
Thus, we would apply the formula:
tan Ѳ = opposite length/adjacent length
[tex] tan 22 = \frac{30}{x} [/tex]
Multiply both sides by x
[tex] tan 22*x = \frac{30}{x}*x [/tex]
[tex] tan 22*x = 30 [/tex]
[tex] 0.4040*x = 30 [/tex]
Divide both sides by 0.4040 to make x the subject of the formula
[tex] \frac{0.4040*x}{0.4040} = \frac{30}{0.4040} [/tex]
[tex] x = \frac{30}{0.4040} [/tex]
[tex] x = 74.26 [/tex]
x ≈ 74.3 (to the nearest tenth)
