Altitude

Definition

Altitude of a triangle is a perpendicular segment from a vertex to the line containing the opposite side. It helps in determining the height of the triangle for various calculations.

5 Must Know Facts For Your Next Test

1. In non-right triangles, altitudes can lie inside, outside, or on the triangle depending on its type (acute, obtuse, or right).
2. The Law of Sines can be used to find unknown altitudes in non-right triangles using $\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$.
3. Altitudes intersect at a point called the orthocenter, which may lie inside or outside the triangle based on its type.
4. To find an altitude using trigonometry, you can use $h = b \cdot \sin(A)$ where $b$ is one side and $A$ is the angle opposite to it.
5. Altitudes are crucial for calculating areas of non-right triangles using $\text{Area} = \frac{1}{2} \cdot base \cdot height$.

Review Questions

• How do you determine whether an altitude lies inside or outside a triangle?
• What role does the Law of Sines play in finding altitudes in non-right triangles?
• Where do all the altitudes of a triangle intersect?

Related terms

Orthocenter: The point where all three altitudes of a triangle intersect.

Law of Sines:

$\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$, relates sides and angles in any triangle.

Height: The perpendicular distance from a vertex to the line containing the opposite side.