Practice problems of the triangle - page 28 of 116
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. The sum of the measures of the interior angles of a triangle is always 180 degrees. An exterior angle of a triangle is an angle that is a linear pair (and hence supplementary) to an interior angle. The best known area formula is T = a*h /2 where a is the length of the side of the triangle, and h is the height or altitude of the triangle.Number of problems found: 2311
- Side lengths
In the triangle ABC, the height to side a is 6cm. The height to side b is equal to 9 cm. Side "a" is 4 cm longer than side "b". Calculate the side lengths a, b. - 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 at the same time. - Sides of right angled triangle
One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle. - Right-angled 40961
A right-angled triangle ABC has sides a = 5 cm, b = 8 cm. The similar triangle A'B'C' is 2.5 times smaller. Calculate what percentage of the area of triangle ABC is the area of triangle A'B'C'. - Karim
Karim uses a photocopier to enlarge the triangle PQR diagram by 150%. a) Write the ratio of the length of P' Q' to the length of PQ. b) Is the ratio of the length P 'R' to the length PR equal to the ratio of the length P 'Q' to the length PQ? c) Use your - Calculate
Calculate the height of a tree that casts a shadow 22 m long if you know that at the same time, a pillar 2 m high casts a shadow 3 meters long. - Shadow
A meter pole perpendicular to the ground throws a shadow of 40 cm long. The house throws a shadow 6 meters long. What is the height of the house? - Angle in RT
Determine the size of the smallest internal angle of a right triangle whose sides constitute the sizes of consecutive members of arithmetic progressions. - Perpendicular 81837
Two neighboring cottagers have cottages under the forest by the stream. They decided to build a bridge over the stream at a place far from the two huts. The distance between the cottages is 230 m; one cottage is 120 m from the stream, and the other is 85 - Isosceles 67744
Two isosceles triangles have the same angle at the vertex opposite the base. The first one has a base of 12 cm and a leg of 9 cm. The other has a 16 cm long base. Calculate the perimeter of the second triangle. - Similar triangles
In the triangle DEF is DE = 21cm, EF = 14.7cm, DF = 28cm. The triangle D'E'F' is similar to the triangle DEF. Calculate the lengths of the sides of the triangle D'E'F' if the similarity coefficient is one-seventh. - Shadow 7838
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? - Hypotenuse 4221
Find the set of points formed by the center of gravity of right triangles with the same hypotenuse (build several possible triangles into one image). - Equilateral 7962
After a long dinner, inside a lounge in the shape of a square ABCD, a drunken shopper E lies in such a way that the triangle DEC is equilateral. Spy F lies on the edge of BC, with |EB|=|EF|. What is the size of the angle CEF? - Draw SSA triangle
Draw a triangle ABC if you know: alpha = 60° side b = 4 cm side a = 10 cm - Two similar
Two similar triangles, one has a circumference of 100 cm, the second has sides successively 8 cm, 14 cm, and 18 cm longer than the first. Find the lengths of its sides. - As shown
As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6, then the perimeter of △ BDE - Triangle 80994
In the triangle, ABC, the angles alpha and beta axes subtend the angle phi = R + gamma/2. R is a right angle of 90°. Verify. - Triangles 6682
Triangles ABC and A'B'C'. They are similar. In triangle ABC, the measures of two angles are 25 degrees and 65 degrees. Explain why in triangle A'B'C' the sum of the sizes of the two angles is equal to 90 degrees - Triangles 2737
The triangles ABC and XYZ are similar. Find the missing lengths of the sides of the triangles. a = 5cm, b = 8cm x = 7.5cm z = 9cm
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