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

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, 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.

  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?