Triangle practice problems - page 40 of 126
Number of problems found: 2520
- Space vectors 3D
The vectors u = (1; 3;- 4) and v = (0; 1; 1) are given. Find their sizes, calculate their angles, and determine the distances between them. - Construction
Construct the triangle ABC if you know: the size of the side AC is 6 cm, the size of the angle ACB is 60°, and the distance of the center of gravity T from the vertex A is 4 cm. (Sketch, analysis, notation of construction, construction) - A cliff
A line from the top of a cliff to the ground passes just over the top of a pole 5 ft high. It meets the ground at a point 8 ft from the base of the pole. The point is 93 ft from the base of the cliff. How high is the cliff? - Similar triangles
The triangles ABC and XYZ are similar. Find the unknown lengths of the sides of the triangles. a) a = 5 cm b = 8 cm x = 7.5 cm z = 9 cm b) a = 9 cm c = 12 cm y = 10 cm z = 8 cm c) b = 4 cm c = 8 cm x = 4.5 cm z = 6 cm - Ruler
Peter is looking at John over a ruler that keeps at an arm's distance of 60 cm from the eye, and on the ruler, John measured the height of 15 mm. John is 2 meters high. How far from Peter stands John? - Triangle construction
Construct a triangle ABC, given the lengths of the sides: c = 8 cm, a = 5 cm and height length hc = 3.5 cm. Perform an analysis, write down the design procedure, perform it, and determine the number of solutions. - Tree height
A tree with an unknown height casts a shadow 18 m long at a time, while a two-meter pole casts a shadow of 2.4 m. How tall is the tree? - Inclined plane
On the inclined plane with an inclination angle of 30°, we will put the body (fixed point) with mass 9 kg. Determine the acceleration of the body motion on an inclined plane. - Segments on the hypotenuse
A right triangle ABC has a hypotenuse c = 26 cm. The altitude from C to the hypotenuse is h_c = 12 cm. What are the lengths of the two segments of the hypotenuse? What are the lengths of sides a and b? What are the angles at vertices A and B? - Compute 4
Compute the exact value of the triangle area with sides 14 mi, 12 mi, and 12 mi long. - Broken tree
The tree was 35 meters high. The tree broke at a height of 10 m above the ground. Top, but does not fall off. It is refuted on the ground. How far from the base of the tree lay its peak? - Vector coordinate calculation
The triangle ABC is given in the plane. A (-3,5), B (2,3), C (-1, -2) write the coordinates of the vectors u, v, w if u = AB, v = AC, and w = BC. Enter the coordinates of the centers of the lines SAB (..), SAC (...), SBC (. ..) - Lookout tower
Calculate the height of a lookout tower forming a shadow of 36 m if a column 2.5 m high has a shadow of 1.5 m simultaneously. - Tree Height Shadow Length
A man 1.65 m tall casts a shadow of 1.25 m. How tall is the tree whose shadow is in debt 2.58 m? - Triangle SSA
Construct a triangle ABC if |AB| = 5 cm va = 3 cm, CAB = 50 °. It is to create the analysis and construction steps. - Triangle area angle
The area of a right triangle ABC is 346 cm2, and the angle at vertex A is 64°. Calculate the lengths of the overhangs a and b. - The ladder and wall
A 6.5-meter-long ladder rests against a vertical wall. Its lower end rests on the ground 1.6 meters from the wall. Determine how high the top of the ladder reaches and at what angle it rests against the wall. - RT area
A right triangle has an area of 54 cm². Calculate the sizes of both legs if the shorter leg is 75% of the size of the longer leg. - Mast rope anchoring
The mast is 190 m high and is attached to six ropes which are anchored in the ground at a distance of 20 m from the base of the mast. How many meters of rope were needed? - Street lamp ladder
The street lamp is 5.5 m high. It suddenly stopped shining. How long do ladders need workers if they know that dedicated lamps can be placed at a distance of 18 dm at the bottom?
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