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EXAMPLE 5 Find the area of a triangle Biology Black-necked stilts are birds that live throughout Florida and surrounding areas but breed mostly in the triangular region shown on the map. Find the area of this region.

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EXAMPLE 5 Find the area of a triangle SOLUTION The area of the region is: Area = bc sin A 1 2 1 2 = (125) (223) sin 54.2° 11,300 Write area formula. Substitute. Use a calculator. The area of the region is about 11,300 square miles. ANSWER

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GUIDED PRACTICE for Example 5 Find the area of ABC with the given side lengths and included angle. 7. a = 10, b = 14, C = 46° SOLUTION The area of the region is: Area = ab sin C 1 2 1 2 = (10) (14) sin 46° 50.4 Write area formula. Substitute. Use a calculator. The area of the region is about 50.4 square units. ANSWER

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GUIDED PRACTICE for Example 5 Find the area of ABC with the given side lengths and included angle. 8. a = 19, c = 8, B = 75° SOLUTION The area of the region is: Area = ac sin B 1 2 1 2 = (19) (8) sin 75° 73.4 Write area formula. Substitute. Use a calculator. The area of the region is about 73.4 square units. ANSWER

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GUIDED PRACTICE for Example 5 Find the area of ABC with the given side lengths and included angle. 9. b = 11, c = 7, A = 120° SOLUTION The area of the region is: Area = bc sin A 1 2 1 2 = (11) (7) sin 120° 33.3 Write area formula. Substitute. Use a calculator. The area of the region is about 33.3 square units. ANSWER

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GUIDED PRACTICE for Example 5 Find the area of ABC with the given side lengths and included angle. 10. a = 20, b = 24, C = 87° SOLUTION The area of the region is: Area = ab sin C 1 2 1 2 = (20) (24) sin 87° 239.7 Write area formula. Substitute. Use a calculator. The area of the region is about 239.7 square units. ANSWER

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