Question
Drawing Triangles
4 of 44 of 4 Questions
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.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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.**
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.**
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