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8-13.

Triangle A, B, C with side B, C, 8. Sides A, B, and A, C, have 1 tick mark each. Angle A measures 36 degrees.Tromika wants to calculate the area of the isosceles triangle at right. 

  1. She decides to start by drawing a height from vertex to side as shown below. Will the two smaller triangles be congruent? In other words, is ? Why or why not?

    Triangle, A B C, dashed segment from vertex A, perpendicular to side, B C, at point, D,  Side, B C, labeled 8,  Angle, B A C, labeled 36 degrees, Sides, A B, & A C, each have 1 tick mark.

    Look at the two triangles that are created. They share a side, and the ticks marks mean the sides are equal. How could they be congruent?

    Yes, they are congruent by .

  2. What is ? ?

    If the segment (height) bisects both and segment , how can you calculate the measure of half of each?

      

  3. Determine . Show how you got your answer.

    Which trig ratio can you use to determine this length?

  4. Calculate the area of .

    How do you find the area of a triangle? Do you have enough information to calculate the area?