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Below is a schematic of a type of bridge design called the Baltimore Truss. It’s composed of various sizes of right triangles that reinforce each other, providing excellent structural integrity while under heavy weight loads. For this reason, the Baltimore truss design is frequently used for railroad bridges.
The height of the Baltimore truss bridge below is 12m. The vertical beams are equally spaced throughout the bridge. The distance of each end of the bridge to the closest vertical beam is the same as the distance between vertical beams. The length of the road 54m, and the length of the top of the bridge is 36m.
What is the length of line segment AB?
Given the dimensions of the bridge in question 1, what is the area of \(\)triangle ABD in square meters?
\(\overline{CE}\) bisects \(\overline{BD}\). What is the area of diamond CFBE?
What is the perimeter of the shaded region shown, in meters?
What is the area of the shaded region shown, in square meters?
Photo by Nina Aldin Thune
The Great Pyramid of Giza is, in a geometric sense, a square pyramid. It has a square base and four triangular faces each meeting at the apex. From just measuring the length of the sides of the base and the overall height of the structure, we can calculate the rest of the dimensions of the pyramid!
A measurement of length commonly used in the ancient world was the cubit. 1 cubit was about the length of an average person’s forearm and, for the Egyptians, equaled approximately 52-53 cm. For ease of calculation, we will keep all our measurements in cubits.
The length of the square base of the Great Pyramid of giza is 440 cubits. Find the length of the diagonal of the square base.
What is the length of the perpendicular bisector of the diagonal of the base of the Great Pyramid, as shown below?
The height of the Great Pyramid of Giza is 280 cubits. What is the length of the edges of its triangular faces, rounded to the nearest cubit?
Each face of the Great Pyramid is what kind of triangle?
Calculate the total surface area (to the nearest square cubit) of the Great Pyramid of Giza, including its base, assuming each face is perfectly flat.
Artists have used triangles in their compositions throughout history. You don’t have to look far to find them in paintings, photographs, sculptures, and more. Triangles often give works of art a sense of stability. An interesting example is included in the anti-war painting “Guernica” by Pablo Picasso (below). Picasso created the painting in 1937 in response to the bombing of the Basque Country town of Guernica (Gernika) by Nazi Germany and Fascist Italy, which were allies of the Spanish Nationalists during the Spanish Civil War.
The composition of the painting has a large triangular shape in the middle created by the light coming down from the candle in the top-center of the canvas. Although Picasso is depicting the chaos and brutality of war, the horror feels almost frozen, in part because of the stabilizing effect of the triangle.
If angle ABC is 100 degrees, and angle FBG is 49 degrees, what is angle BAD?
If BG is 12 inches, GC is 4 inches, and BF is 9 inches, how long is FD?
If AC is 19 inches, how long is AB to the nearest hundredth of an inch?