Answer:
GIVEN :-
- ∠A = 15°
- Length of AB (hypotenuse) = 60 ft
TO FIND :-
- Length of BC
- Length of AC
- Area of ΔABC
FACTS TO KNOW BEFORE SOLVING :-
- [tex]\sin \theta = \frac{Side \: opposite \: to \: \theta}{Hypotenuse}[/tex]
- [tex]\cos \theta = \frac{Side \: adjacent \: to \: \theta}{Hypotenuse}[/tex]
SOLUTION :-
In ΔABC ,
- [tex]\sin 15 = \frac{BC}{60}[/tex]
[tex]=> 0.2588... = \frac{BC}{60}[/tex]
[tex]=> BC = (0.2588....) \times 60 = 15.5291.....[/tex] ≈ 15.5 ft
- [tex]\cos 15 = \frac{AC}{60}[/tex]
[tex]=> 0.9659..... = \frac{AC}{60}[/tex]
[tex]=> AC = (0.9659.....) \times 60 = 57.9555.....[/tex] ≈ 58 ft
Area of ΔABC = [tex]\frac{1}{2} \times 58 \times 15.5 = 449.5 \:ft^2[/tex]
