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Home > CCG > Chapter 4 > Lesson 4.1.4 > Problem 4-40

4-40.

Use the relationships in the diagrams below to write an equation and solve for .  

  1. A right triangle with a base of 18, height of x and and hypotenuse of 30.

     

    This is a right triangle, so use the Pythagorean Theorem to solve for .

  1. Four adjacent angles together form a 360 degree angle. The angles starting at the top left going clockwise are 2, x, &, x, &, 3, x + 20 degrees, and 2, x + 20 degrees.

    What is the sum of these angles?
    How can you use the sum of the angles to write an equation and solve for ?

  1. One triangle has an angle, 20 degrees, between the sides 5, and 12. The angle opposite the 12 side is 146.8 degrees. A second triangle has an angle, 20 degrees, between the sides x, and 3. The angle opposite the, x, side is 146.8 degrees.

    Are these triangles similar?
    If so, how can you use their similarity to write an equation and solve for ?