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Home > GC > Chapter 7 > Lesson 7.2.3 > Problem 7-68


Tromika wants to find the area of the isosceles triangle below.  

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.

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

    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 .

Triangle A, B, C. A line is drawn from vertex A  perpendicular to side B, C at point, D.  Side B, Chas a length of 8.  Angle B, A, C is 36 degrees.  Sides A, B and Side A, C have 1 tick mark.

  1. What is ? ?

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

  2. Find . Show how you got your answer.

    Which trig ratio can you use to determine this length?

  3. Find the area of .

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