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Drawing Triangles

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Question
A triangle has one side with a length of 13.
Across from the side with the length of 13
is an angle with the measure of 90∘.

Which triangle matches the description?

Responses

Triangle ABC where angle A equals 67.4 degrees, angle B equals 90 degrees, angle C equals 22.6 degrees, side A B equals 5, side B C equals 12, & side A C equals 13.
© 2018 StrongMind. Created using GeoGebra.
Image with alt text: Triangle ABC where angle A equals 67.4 degrees, angle B equals 90 degrees, angle C equals 22.6 degrees, side A B equals 5, side B C equals 12, & side A C equals 13. © 2018 StrongMind. Created using GeoGebra.

Triangle ABC where angle A equals 30 degrees, angle B equals 90 degrees, angle C equals 60 degrees, side A B equals 13, side B C equals 7.5, & side A C equals 15.
© 2018 StrongMind. Created using GeoGebra.
Image with alt text: Triangle ABC where angle A equals 30 degrees, angle B equals 90 degrees, angle C equals 60 degrees, side A B equals 13, side B C equals 7.5, & side A C equals 15. © 2018 StrongMind. Created using GeoGebra.

Triangle ABC where angle A equals 22.6 degrees, angle B equals 90 degrees, angle C equals 67.4 degrees, side A B equals 13, side B C equals 5.4, & side A C equals 14.1.
© 2018 StrongMind. Created using GeoGebra.

1 answer

To determine which triangle matches the description given, let's analyze the details provided:

  1. One side with length 13: This describes one of the sides of the triangle.
  2. The angle across from this side is 90 degrees: This indicates that the triangle is a right triangle, specifically making the side with length 13 the hypotenuse.

Based on this information, we need to find the triangle from the responses that has:

  • A side of length 13
  • A right angle (90 degrees) opposite this side.

Let's examine the options:

  1. Triangle ABC where angle A equals 67.4 degrees, angle B equals 90 degrees, angle C equals 22.6 degrees, side A B equals 5, side B C equals 12, & side A C equals 13.

    • Here, side A C (length 13) is opposite angle B (90 degrees). Therefore, this triangle matches the description.

  2. Triangle ABC where angle A equals 30 degrees, angle B equals 90 degrees, angle C equals 60 degrees, side A B equals 13, side B C equals 7.5, & side A C equals 15.

    • The longest side here (hypotenuse) is side A C, which is 15, not 13, so this does not match.

  3. Triangle ABC where angle A equals 22.6 degrees, angle B equals 90 degrees, angle C equals 67.4 degrees, side A B equals 13, side B C equals 5.4, & side A C equals 14.1.

    • In this triangle, side A B (which is 13) is opposite angle A (not across from the 90-degree angle), so it does not match the description provided.

Thus, the correct triangle that matches the description you provided is:

Triangle ABC where angle A equals 67.4 degrees, angle B equals 90 degrees, angle C equals 22.6 degrees, side A B equals 5, side B C equals 12, & side A C equals 13.