Question

Find the area using sine rules.

Answer 1

Answer:

• 22.44 mi²

Step-by-step 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 = $\sqrt{s(s - a)(s - b)(s - c)}$, 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 = $\sqrt{12(12 - 5.9)(12 - 7.7)( 12 - 10.4)}$ = 22.44 mi²