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Home > CCG > Chapter 5 > Lesson 5.3.5 > Problem 5-135

5-135.

Triangle A, B, C. Angle A is 45 degrees and angle C is 30 degrees. Two internal triangles are created by a dashed line segment of 4 drawn from the upper vertex perpendicular to the base.Find the area and perimeter of at right. Give approximate (decimal) answers, not exact answers.  

Separate into two separate triangles by dropping the height from vertex .
Label the new point , creating and .

Point added, labeled, d, where the vertical line segment, intersects side, A, C, triangle, A, B, D, is shaded blue, & right triangle, B, C, D, is shaded red.

Both of the triangles that have been created are special right triangles, because the height creates two right triangles: a triangle and a triangle.

The length of the hypotenuse in a  triangle is the length of a leg times .
In a  triangle, the length of the side opposite the  angle is half of the length of the hypotenuse and the length of the side opposite the  angle is half of the length of the hypotenuse times .