# Pythagorean theorem - examples - page 16

1. Angles by cosine law Calculate the size of the angles of the triangle ABC, if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem).
2. Inscribed circle XYZ is right triangle with right angle at the vertex X that has inscribed circle with a radius 5 cm. Determine area of the triangle XYZ if XZ = 14 cm.
3. Minute Two boys started from one place. First went north at velocity 3 m/s and the second to the east with velocity 4 m/s. How far apart they are after minute?
4. Roof 7 The roof has the shape of a regular quadrangular pyramid with a base edge of 12 m and a height of 4 m. How many percent is folds and waste if in construction was consumed 181.4m2 of plate?
5. Rhumbline Find circumference and area of the rhumbline ABCD if the short side AD of which has a length of 5 cm, and the heel of the height from D leading to the AB side divides the AB side into two sections of 3 cm and 4 cm.
6. The chord Calculate a chord length which the distance from the center of the circle (S, 6 cm) equals 3 cm.
7. Concrete block Determine the volume of concrete block whose one edge of the base has a length 3 meters, body diagonal is 13 meters and its height is 12 meters.
8. Acceleration 2 if a car traveling at a velocity of 80 m/s/south accelerated to a velocity of 100 m/s east in 5 seconds, what is the cars acceleration? using Pythagorean theorem
9. Right triangle It is given a right triangle angle alpha of 90 degrees beta angle of 55 degrees c = 10 cm use Pythagorean theorem to calculate sides a and b
10. Pyramid 4sides Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the height of the pyramid is 7 cm.
11. Chord 5 It is given circle k / S; 5 cm /. Its chord MN is 3 cm away from the center of the circle . Calculate its length.
12. Prism Find the volume and surface area of prism with base of an equilateral triangle with side 7 dm long and the body height of 1.5 m.
13. Diagonal - simple Calculate the length of the diagonal of a rectangle with dimensions 5 cm and 12 cm.
14. Cube diagonals Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
15. Quadrilateral 2 Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles.
16. 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 refuted on the ground. How far from the base of the tree lay its peak?
17. Right angled triangle Hypotenuse of a right triangle is 17 cm long. When we decrease length of legs by 3 cm then decrease its hypotenuse by 4 cm. Determine the size of legs.
18. Cube Calculate the surface of the cube ABCDA'B'C'D' if the area of rectangle ACC'A' = 344 mm2.
19. Drainage channel The cross section of the drainage channel is an isosceles trapezoid whose bases have a length of 1.80 m, 0.90 m and arm has length 0.60 meters. Calculate the depth of the channel.
20. Bearing A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point.

Do you have an interesting mathematical example that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.

Pythagorean theorem is the base for the right triangle calculator.