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Home > GC > Chapter 8 > Lesson 8.3.1 > Problem 8-86


For each triangle below, find the value of , if possible. Name the triangle tool that you used. If the triangle cannot exist, explain why.  

  1. A right triangle with a leg, X, and hypotenuse of 28. The side opposite the 60 degree angle is, X.

    What special kind of triangle is this? How can this help you find ?

  1. A triangle with side lengths, 7, and, x. The angle opposite the side, x, is 50 degrees. The angle opposite the side, 7, is 68 degrees.

    Use the Law of Sines to solve for .

  1. A right triangle with a height of 19, base of X, and hypotenuse of 17.

    Use the Pythagorean Theorem to find .

    There is no solution, because the hypotenuse must be the longest side.

  1. An obtuse triangle with a base of 8.  An external triangle is created, by a line segment of X, drawn from the upper vertex, to the extended base, at right angles.
    Area of the shaded region is  square units.

    What is the formula for the area of a triangle?