Two sides and the enclosed angle for a triangle are 3, 6, 30 degrees. What is the area of the triangle.

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justaguide eNotes educator| Certified Educator

The length of two sides of a triangle and the angle between the two sides is given. The length of the sides is 3 and 6. The angle between them is 30 degrees.

Take the side with length 6 as the base. To determine the area of the triangle the length of the base (b) and height (h) are required. The area is (1/2)*b*h. Drop a perpendicular from the end of the side with length 3 to the side with length 6. An equilateral triangle is formed with hypotenuse 3. If the height is h, h/3 = sin 30

h = 3*sin 30 = 1.5

The area of the triangle is (1/2)*6*1.5 = 4.5 square units.