An isosceles triangle has two equal sides of 4 cm. The angle between these sides is 30 degree. Find the area of the triangle
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We can use the formula 2 1 ( b a s e ) ( h e i g h t ) to find the area of this triangle.
First we need to get the values of the other angles of the triangle. Since it's an isosceles triangle, we know that both of the other angles are equal. Since we also know that the sum of all angles in any triangle must be 180, we can solve using 2 θ + 3 0 = 1 8 0 and find that both of the other angles are 75 degrees.
Using the side of unknown length as the base, we determine the height of the triangle to be 4 s i n 7 5 , the "vertical" distance travelled by the given sides. The base of the triangle is ( 2 ) ( 4 c o s 7 5 ) , since that is the combined "horizontal" distance that the two given sides span.
Plugging into the area of a triangle formula, we find 2 1 ( 8 c o s 7 5 ) ( 4 s i n 7 5 ) = 4