Triangle altitude

Triangle. A = bhJ2, where b denotes the base and h the altitude. 

Triangles (see also Tlane Trigonometry ) A = V2hh where h = base, h = altitude. 

Two or more lines are concurrent if there is a single point which lies on all of them. The three altitudes of a triangle (if taken as lines, not segments) are always concurrent, and their point of concurrency is called the orthocenter. The angle bisectors of a triangle are concurrent at a point equidistant from their sides, and the medians are concurrent two thirds of the way along each median from the vertex to the opposite side. The point of concurrency of the medians is the centroid. 

Figure 9. Zonal/seasonal averages of aerosol volume density V as a function of altitude and latitude. Dotted lines mark the tropopause plus 2 kilometers. Upward-pointing triangles on the x-axis mark the eruptions of Kelut (Feb. 1990 - 8 S), Knatubo (Jun. 1991 - 15 N) and Hudson (Aug. 1991 - 46 S).

Fig. 2 Stations used in measurements of aerosol number size distributions. Black symbols are EUSAAR stations, white GUAN (MPZ was in both networks). Triangles denote high-altitude mountain stations (over 1,000 m from mean sea level). Figure adapted from figure published in [18], which also has more details on the locations and types of the stations...

The altitude of a triangle is the line segment from one vertex that is perpendicular to the opposite side, amicable numbers... 

The intersection of an altitude of a triangle with the base to which it is drawn, foot of line... 

The triangle whose vertices are the feet of the altitudes of a given triangle, orthocenter... 

This is actually the top one fourth of a full ternary diagram of the Cur-Sn-Fb system and includes compositions with 50-100% copper. The heavy lines intersect at the 87-10-3 composition. Contours of equal Cu composition are shown as solid horizontal lines, Sn as dotted lines with positive slope, and Pb as light solid lines with negative slope. If the heavy intersecting lines are extended parallel to these contours, they intersect the sides of the triangle at 87% towards the Cu vertex, 10% towards the Sn vertex, and 3% towards the Pb vertex. Altitude lengths can also be used to determine the composition al = Cu% a2 = Sn% o3 = Pb% al + a2 + = 100%. For... 

Compute the area of a triangle (according to the formula A = ba) if its base and altitude are measured to equal 42.07 cm and 16.0 cm, respectively. Justify the number of significant figures in the answer. 

Figure 7.25. Percentage abundance of proton hydrates (PH) and nonproton hydrates (NPH) as a function of altitude at 45°N. The full line indicates model values and dots and triangles are experimental data. From Beig et al. (1993a).

E20.7(b) The volume of a hexagonal unit cell is the area of the base times the height c. The base is equivalent to two equilateral triangles of side a. The altitude of such a triangle is a sin 60°. So the volume is... 

The moment of inertia about the axis of the altitude of the triangle (z-axis) is... 

That is to say, the height of the rectangle must be half the altitude of the triangle. 

To use Eq. 2.23 we look up the centroid of a triangle about its base and find that it is one-third of its altitude and that its area is its base times one-half of its altitude so... 

Any point on the interior of the triangle, such as point P in Figure H.1, represents a ternary mixture. To obtain the composition of the mixture at P, drop perpendiculars flP, fcP, and cP to each of the three edges. In an equilateral triangle the lengths of these perpendiculars always sum to the altitude of the triangle, hA,... 

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