9.5 Apply the Law of Sinesday 3

How do you use the law of sines to find the area of a triangle?

When you know the lengths of two sides and the measure of the included angles, you can find the area of a triangle.

Find the Area of a Triangle

BiologyBlack-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.

SOLUTION

The area of the region is:

Area = bc sin A12

12= (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

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 C1212= (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

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 B1

212= (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

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 A1212= (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

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 C1212= (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

How do you use the law of sines to find the area of a triangle?

𝐴𝑟𝑒𝑎=12𝑏𝑐𝑠𝑖𝑛𝐴

𝐴𝑟𝑒𝑎=12𝑎𝑐𝑠𝑖𝑛𝐵

𝐴𝑟𝑒𝑎=12𝑎𝑏𝑠𝑖𝑛𝐶

9.5 Assignment, day 3

p. 590, 29-41 allNo work is the same as a missing problem.