Solve each problem. (Source for Exercises 49 and 50: Parker, M., ...

Question

Solve each problem. (Source for Exercises 49 and 50: Parker, M., Editor, She Does Math, Mathematical Association of America.)

Length of Sides of an Isosceles Triangle An isosceles triangle has a base of length 49.28 m. The angle opposite the base is 58.746°. Find the length of each of the two equal sides.

Accepted Answer

Determine the measure of two equal sides of an isosceles triangle. If the base side is 45.36 m and the angle opposite to the base side is 45.582 degrees. But we have four possible answers. All just different measures and meters. Now to solve this, let's first draw our triangle. We have an iso triangle which means two sides will be the same length. Now, the base we know is 45.36 m and its opposite angle is 45.582 degrees. Let's label this ABC. Now to solve this, we can divide this triangle in half and split it up into two equivalent right triangles. No, our angles and our sides will both be bisected in half. So I will label our next point point D for the middle where side CD will be 45.36 divided by two. This is 22.68 and it's the same for both sets. Our angles are also split in half. So we have 45.582 divided by two, which gives the angle 22.7 91 degrees. I will now redraw the strangle, we have an angle of 22.791 and a side length of 22.68. We just need to find our missing side ac as we want one of the side lengths of the triangle of the Aso triangle. I should say which movie you want to find their ipod news. We can do this using sign sign of an angle. The angle A will be our opposite side divided by a high. That would be 22.68 divided by a size AC. Now we have angle A which is 22.791. We can rearrange to get ac equals 22.68 divided by sine 22.791. We can plug this into the calculator which gives us the answer 58.55 m. This means the answer to our problem is answer A OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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