Answer:
Explanation:
Step 1
Find the missing angle:
- m∠H = 180° - (47° + 99°) = 34°
Step 2
Find the missing sides by using the law of sines:
- sin 34° / 5.9 = sin 47° / HP = sin 99° / HK
- HP = 5.9 sin 47°/sin 34° = 7.7 mi
- HK = 5.9 sin 99° / sin 34° = 10.4 mi
Step 3
Use Heron's formula for the area:
- A =
, where s is semi-perimeter, and a, b, c - sides
Find s:
- s = 1/2(5.9 + 7.7 + 10.4) = 12
Find A:
- A =
= 22.44 mi²