(a) A gardener has a rectangular plot measuring 3.0 m × 4.0 m. She wishes to use half of this area to make a triangular flower bed. Of the two types of triangles shown in Figure 1.12, which should she use to do this: (1) the right triangle, (2) the isosceles triangle – two sides equal, or (3) either one?

(b) In laying out the flower bed, the gardener decides to use a right triangle. Wishing to line the sides with rows of stone, she wants to know the total length (L) of the triangle sides. She would also like to know the values of the acute angles of the triangle. Can you help her so she doesn’t have to do physical measurements? (Appendix I includes a review of trigonometric relationships.)

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4.0 m Right triangle 3.0 m 4.0 m Isosceles triangle 3.0 m FIGURE 1.12 A flower bed project Two types of triangles for a new flower bed. See Example 1.10.