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Home > GC > Chapter 4 > Lesson 4.2.1 > Problem 4-56

4-56.

For each diagram below, solve for . Name the relationship(s) you used. Show all work.  

  1. Two right triangles connected to each other, The smaller triangle's hypotenuse is the short leg of the larger triangle, The smaller triangle has legs of 3 and 4 meters, The larger triangle has a long leg of 12 meters, and a hypotenuse of, x.

    Use the Pythagorean Theorem to solve for .

    Y is the hypotenuse of the smaller right triangle but one of the legs of the large right triangle.

    After solving for , use the Pythagorean Theorem again to solve for .

  1. A triangle where one of the base angles is 35 degrees. The top vertex angle is 65 degrees.  Two line segments parallel to the base extend first from the left side toward the left and the second from the right side toward the right  creating angles of 35 and x degrees with the triangle sides.

    Extend the parallel lines that have already been drawn.

    A triangle with the base, a horizontal line starting from a point near the bottom right side of the triangle and going right, and another horizontal line starting near the top left of the triangle and going left, which are all parallel to each other. The bottom left angle is 35 degrees & the top angle is 65 degrees.

    Now establish a relationship between and one of the angles that has already been given.

    Use the Math Notes boxes in Lessons 2.1.1 and 2.1.4 if you need help remembering angle pair relationships.