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

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 :-

• $\sin \theta = \frac{Side \: opposite \: to \: \theta}{Hypotenuse}$
• $\cos \theta = \frac{Side \: adjacent \: to \: \theta}{Hypotenuse}$

SOLUTION :-

In ΔABC ,

• $\sin 15 = \frac{BC}{60}$

$=> 0.2588... = \frac{BC}{60}$

$=> BC = (0.2588....) \times 60 = 15.5291.....$ ≈ 15.5 ft

• $\cos 15 = \frac{AC}{60}$

$=> 0.9659..... = \frac{AC}{60}$

$=> AC = (0.9659.....) \times 60 = 57.9555.....$ ≈ 58 ft

Area of ΔABC = $\frac{1}{2} \times 58 \times 15.5 = 449.5 \:ft^2$