Questions: On Your Own 3. MP Reason A graphic designer wants to reproduce the logo of a mountain-climbing club for some club stationery. The logo is a triangle with the angles shown. A. The designer wants the base to be 2 inches long. How should the triangle be drawn?

Solution Steps

The problem states that the triangle has angles of 50°, 60°, and 70°. The designer wants the base of the triangle to be 2 inches long. The problem asks how the triangle should be drawn. Since all three angles are given, and one side is specified, the triangle can be uniquely drawn.

It does not matter which side is chosen as the base. Suppose the side opposite the 70° angle is chosen as the base. Let the sides opposite the 50°, 60°, and 70° angles be _a_, _b_, and _c_ respectively. So, _c_ = 2 inches.

The Law of Sines states that the ratio of the length of a side to the sine of the angle opposite that side is the same for all three sides of a triangle. Thus:

a / sin(50°) = b / sin(60°) = c / sin(70°)

We know c = 2, so we can find _a_ and _b_ using:

a = c * sin(50°) / sin(70°) ≈ 2 * 0.766 / 0.940 ≈ 1.63 inches

b = c * sin(60°) / sin(70°) ≈ 2 * 0.866 / 0.940 ≈ 1.84 inches

Final Answer: