Right triangle - 9th grade (14y) - examples - page 14

1. Cube wall
The perimeter of one cube wall is 120 meters. Calculate the surface area and the body diagonal of this cube.
2. Isosceles trapezoid
Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high.
3. Circle and rectangle
A rectangle with sides of 11.7 cm and 175 mm is described by circle. What is its length? Calculate the content area of the circle described by this circle.
4. Diagonals
Draw a square ABCD whose diagonals have a length of 6 cm
5. Is right?
Determine whether the triangle with legs (catheti) 19.5 cm and 26 cm and length of the hypotenuse 32.5 cm is rectangular?
6. 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.
7. Lift
The largest angle at which the lift rises is 16°31'. Give climb angle in permille.
8. 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?
9. 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.
10. 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.
11. 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
12. Isosceles right triangle
Contents of an isosceles right triangle is 18 dm2. Calculate the length of its base.
13. Chord 2
Point A has distance 13 cm from the center of the circle with radius r = 5 cm. Calculate the length of the chord connecting the points T1 and T2 of contact of tangents led from point A to the circle.
14. 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.
15. 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
16. Cube diagonals
Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
17. Diagonal - simple
Calculate the length of the diagonal of a rectangle with dimensions 5 cm and 12 cm.
Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles.
19. 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?
20. Cube
Calculate the surface of the cube ABCDA'B'C'D' if the area of rectangle ACC'A' = 344 mm2.

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