H is the orthocenter of AABC. We know AB = AC = BC/ V3. What is ZBHC?

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
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**Problem Statement:**

\( H \) is the orthocenter of \(\triangle ABC\). We know \( AB = AC = \frac{BC}{\sqrt{3}} \). What is \(\angle BHC\)?

**Explanation:**

In this problem, we are dealing with triangle \(\triangle ABC\) for which point \( H \) is identified as the orthocenter. An orthocenter is the point where all the altitudes of a triangle intersect.

We are given specific relationships between the sides of the triangle:
- Sides \( AB \) and \( AC \) are equal, indicating that triangle \(\triangle ABC\) could be isosceles with respect to these sides.
- Side \( BC \) is \(\sqrt{3}\) times longer than sides \( AB \) and \( AC\), providing a scalar relationship useful for solving the angle \(\angle BHC\).

The problem asks for the measure of the angle \(\angle BHC\). This requires understanding the geometric properties of the triangle and applying trigonometric or orthocentric properties to solve for the angle.
Transcribed Image Text:**Problem Statement:** \( H \) is the orthocenter of \(\triangle ABC\). We know \( AB = AC = \frac{BC}{\sqrt{3}} \). What is \(\angle BHC\)? **Explanation:** In this problem, we are dealing with triangle \(\triangle ABC\) for which point \( H \) is identified as the orthocenter. An orthocenter is the point where all the altitudes of a triangle intersect. We are given specific relationships between the sides of the triangle: - Sides \( AB \) and \( AC \) are equal, indicating that triangle \(\triangle ABC\) could be isosceles with respect to these sides. - Side \( BC \) is \(\sqrt{3}\) times longer than sides \( AB \) and \( AC\), providing a scalar relationship useful for solving the angle \(\angle BHC\). The problem asks for the measure of the angle \(\angle BHC\). This requires understanding the geometric properties of the triangle and applying trigonometric or orthocentric properties to solve for the angle.
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