Given:  Right △ABC with m∠C=90∘ and m∠A=60∘; AB=28 Find:  BC

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Given:  Right △ABC with m∠C=90∘ and m∠A=60∘; AB=28
Find:  BC

The image depicts a right triangle labeled as triangle ABC. 

- **Vertices:**
  - Point A is at the top of the triangle.
  - Point C is the vertex of the right angle.
  - Point B is at the bottom right.

- **Angle Measurement:**
  - ∠ACB is the right angle (90°).
  - ∠CAB is marked as 60°.

- **Sides:**
  - Side AC is vertical.
  - Side BC is horizontal, forming the base of the triangle.
  - Side AB is the hypotenuse, opposite the right angle.

The triangle demonstrates the properties of a 30-60-90 right triangle, which is a special type of right triangle with interior angles of 30°, 60°, and 90°. These triangles have specific side ratios: the side opposite the 30° angle is half the hypotenuse, and the side opposite the 60° angle is √3/2 times the hypotenuse.
Transcribed Image Text:The image depicts a right triangle labeled as triangle ABC. - **Vertices:** - Point A is at the top of the triangle. - Point C is the vertex of the right angle. - Point B is at the bottom right. - **Angle Measurement:** - ∠ACB is the right angle (90°). - ∠CAB is marked as 60°. - **Sides:** - Side AC is vertical. - Side BC is horizontal, forming the base of the triangle. - Side AB is the hypotenuse, opposite the right angle. The triangle demonstrates the properties of a 30-60-90 right triangle, which is a special type of right triangle with interior angles of 30°, 60°, and 90°. These triangles have specific side ratios: the side opposite the 30° angle is half the hypotenuse, and the side opposite the 60° angle is √3/2 times the hypotenuse.
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