Answer:
TO FIND :-
- Length of all missing sides.
FORMULAES TO KNOW BEFORE SOLVING :-
- [tex]\sin \theta = \frac{Side \: opposite \: to \: \theta}{Hypotenuse}[/tex]
- [tex]\cos \theta = \frac{Side \: adjacent \: to \: \theta}{Hypotenuse}[/tex]
- [tex]\tan \theta = \frac{Side \: opposite \: to \: \theta}{Side \: adjacent \: to \: \theta}[/tex]
SOLUTION :-
1) θ = 16°
Length of side opposite to θ = 7
Hypotenuse = x
[tex]=> \sin 16 = \frac{7}{x}[/tex]
[tex]=> \frac{7}{x} = 0.27563......[/tex]
[tex]=> x = \frac{7}{0.27563....} = 25.39568.....[/tex] ≈ 25.3
2) θ = 29°
Length of side opposite to θ = 6
Hypotenuse = x
[tex]=> \sin 29 = \frac{6}{x}[/tex]
[tex]=> \frac{6}{x} = 0.48480......[/tex]
[tex]=> x = \frac{6}{0.48480....} = 12.37599.....[/tex] ≈ 12.3
3) θ = 30°
Length of side opposite to θ = x
Hypotenuse = 11
[tex]=> \sin 30 = \frac{x}{11}[/tex]
[tex]=> \frac{x}{11} = 0.5[/tex]
[tex]=> x = 0.5 \times 11 = 5.5[/tex]
4) θ = 43°
Length of side adjacent to θ = x
Hypotenuse = 12
[tex]=> \cos 43 = \frac{x}{12}[/tex]
[tex]=> \frac{x}{12} = 0.73135......[/tex]
[tex]=> x = 12 \times 0.73135.... = 8.77624....[/tex] ≈ 8.8
5) θ = 55°
Length of side adjacent to θ = x
Hypotenuse = 6
[tex]=> \cos 55 = \frac{x}{6}[/tex]
[tex]=> \frac{x}{6} = 0.57357......[/tex]
[tex]=> x = 6 \times 0.57357.... = 3.44145....[/tex] ≈ 3.4
6) θ = 73°
Length of side adjacent to θ = 8
Hypotenuse = x
[tex]=> \cos 73 = \frac{8}{x}[/tex]
[tex]=> \frac{8}{x} = 0.29237......[/tex]
[tex]=> x = \frac{8}{0.29237.....} = 27.36242.....[/tex] ≈ 27.3
7) θ = 69°
Length of side opposite to θ = 12
Length of side adjacent to θ = x
[tex]=> \tan 69 = \frac{12}{x}[/tex]
[tex]=> \frac{12}{x} = 2.60508......[/tex]
[tex]=> x = \frac{12}{2.60508....} = 4.60636....[/tex] ≈ 4.6
8) θ = 20°
Length of side opposite to θ = 11
Length of side adjacent to θ = x
[tex]=> \tan 20 = \frac{11}{x}[/tex]
[tex]=> \frac{11}{x} = 0.36397......[/tex]
[tex]=> x = \frac{11}{0.36397....} =30.22225....[/tex] ≈ 30.2
