Question

Use trig to find the legs of ABC if the base is AC and the height is BC (round to nearest tenth)​

Answer 1

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 :-

• 
  `\sin \theta = (Side \: opposite \: to \: \theta)/(Hypotenuse)`
• 
  `\cos \theta = (Side \: adjacent \: to \: \theta)/(Hypotenuse)`

SOLUTION :-

In ΔABC ,

• 
  `\sin 15 = (BC)/(60)`

`=> 0.2588... = (BC)/(60)`

`=> BC = (0.2588....) * 60 = 15.5291.....` ≈ 15.5 ft

• 
  `\cos 15 = (AC)/(60)`

`=> 0.9659..... = (AC)/(60)`

`=> AC = (0.9659.....) * 60 = 57.9555.....` ≈ 58 ft

Area of ΔABC =
`(1)/(2) * 58 * 15.5 = 449.5 \:ft^2`