# Altitudes

Altitudes, the vertical distance above a reference point on the Earth's surface, serve as crucial measures in various fields, from geography and aviation to mountaineering and meteorology. Defined by their elevation above sea level or another reference datum, altitudes provide vital insights into topographical features, atmospheric conditions, and navigational parameters. Understanding altitudes enables us to comprehend the intricacies of terrain, plan efficient transportation routes, and gauge the effects of elevation on climate and human physiology. In this essay, we delve into the significance of altitudes across different disciplines, exploring their utility and implications in diverse contexts.

- What is the orthocenter of a triangle with corners at #(7 ,8 )#, #(3 ,4 )#, and (5 ,6 )#?
- What is the orthocenter of a triangle with corners at #(7 ,3 )#, #(4 ,8 )#, and (6 ,3 )#?
- What is the orthocenter of a triangle with corners at #(2 ,7 )#, #(1 ,1 )#, and (3 ,2 )#?
- A triangle has corners A, B, and C located at #(4 ,5 )#, #(3 ,6 )#, and #(2 ,4 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- What is the orthocenter of a triangle with corners at #(5 ,7 )#, #(2 ,3 )#, and (4 ,5 )#?
- If the altitude of an equilateral triangle is #8sqrt3#, what is the perimeter of the triangle?
- A triangle has corners A, B, and C located at #(2 ,7 )#, #(7 ,5 )#, and #(3 , 2 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- A triangle has corners A, B, and C located at #(2 ,7 )#, #(7 ,4 )#, and #(1 , 2 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- What is the orthocenter of a triangle with corners at #(1 ,4 )#, #(5 ,7 )#, and (2 ,3 )#?
- A triangle has corners A, B, and C located at #(6 ,8 )#, #(7 ,4 )#, and #(5 ,3 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- What is the orthocenter of a triangle with corners at #(1, 3)#, #(6, 2)#, and #(5, 4)#?
- A triangle has corners A, B, and C located at #(7 ,6 )#, #(8 ,3 )#, and #(2 ,1 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- What is the orthocenter of a triangle with corners at #(3 ,1 )#, #(4 ,5 )#, and (2 ,2 )#?
- A triangle has corners A, B, and C located at #(1 ,3 )#, #(9 ,5 )#, and #(6 ,2 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- A triangle has corners A, B, and C located at #(8 ,7 )#, #(1 ,5 )#, and #(6 , 3 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- A triangle has corners A, B, and C located at #(4 ,2 )#, #(3 ,4 )#, and #(6 ,8 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- What is the orthocenter of a triangle with corners at #(2 ,6 )#, #(9 ,1 )#, and (5 ,3 )#?
- What is the orthocenter of a triangle with corners at #(3 ,1 )#, #(1 ,3 )#, and (5 ,2 )#?
- What is the orthocenter of a triangle with corners at #(9 ,7 )#, #(4 ,4 )#, and (8 ,6 )#?
- A triangle has corners A, B, and C located at #(2 ,3 )#, #(5 ,8 )#, and #(3 , 2 )#, respectively. What are the endpoints and length of the altitude going through corner C?