Geometry - examples
- Hypotenuse - RT
A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle?
- A boy
A boy of height 1.7m is standing 30m away from flag staff on the same level ground . He observes that the angle of deviation of the top of flag staff is 30 degree. Calculate the height of flag staff.
- Shadow of tree
Miro stands under a tree and watching its shadow and shadow of the tree. Miro is 180 cm tall and its shade is 1.5 m long. The shadow of the tree is three times as long as Miro's shadow. How tall is the tree in meters?
In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
- Reverse Pythagorean theorem
Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ? Δ DEF: 55 dm, 82 dm, 61 dm ? Δ GHI: 24 mm, 25 mm, 7 mm ? Δ JKL: 32 dm, 51 dm, 82 dm ? Δ MNO: 51 dm, 45 dm, 24 dm ?
Triangle KLM is given by plane coordinates of vertices: K[-2, -20] L[4, 1] M[-16, 4]. Calculate its area and itsinterior angles.
Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters.
- Circular pool
The base of pool is circle with a radius r = 10 m excluding circular segment that determines chord length 10 meters. Pool depth is h = 2m. How many hectoliters of water can fit into the pool?
Are two right triangles similar to each other if the first one has a acute angle 40° and second one has acute angle 50°?
There is regular hexagon ABCDEF. If area of the triangle ABC is 22, what is area of the hexagon ABCDEF? I do not know how to solve it simply....
On the road sign, which informs the climb is 8.7%. Car goes 5 km along this road. What is the height difference that car went?
- Similarity coefficient
The ratio of similarity of two equilateral triangles is 3.5 (ie 7:2). The length of the side of smaller triangle is 2.4 cm. Calculate the perimeter and area of the larger triangle.
- Speed of Slovakian trains
Rudolf decided to take the train from the station 'Trnava' to 'Zemianske Kostoľany'. In the train timetables found train R 725 Remata : km0Bratislava hl.st.12:574Bratislava-Vinohrady13:0113:0219Pezinok13:1213:1346Trnava13:3013:3263Leopoldov13:4514:0168H
Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[11,4] B[13,-7] C[-17,-18].
The rectangular crossroads comes passenger car and an ambulance, the ambulance left. Passenger car is at 43 km/h and ambulance 52 km/h. Calculate such a relative speed of the ambulance moves to the car.
- OK circle
Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 33 and one cathetus long 17.
Road has climbing 1:27. How big is a angle corresponds to this climbing?
- Angle between lines
Calculate the angle between these two lines: ? ?
Within a regular pentagon ABCDE point P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch.
- The chord
Side of the triangle inscribed in a circle is a chord passing through circle center. What size are the internal angles of a triangle, if one of them is 40°?