# Right triangle - 9th grade (14y) - examples - page 19

1. Diagonals
A diagonal of a rhombus is 20 cm long. If it's one side is 26 cm find the length of the other diagonal.
2. Diagonal
he rectangular ABCD trapeze, whose AD arm is perpendicular to the AB and CD bases, has area 15cm square. Bases have lengths AB = 6cm, CD = 4cm. Calculate the length of the AC diagonal.
3. Embankment
Perpendicular cross-section of the embankment around the lake has the shape of an isosceles trapezoid. Calculate the perpendicular cross-section, where bank is 4 m high the upper width is 7 m and the legs are 10 m long.
4. Area of iso-trap
Find the area of an isosceles trapezoid, if the lengths of its bases are 16 cm, and 30 cm, and the diagonals are perpendicular to each other.
5. How far
From the top of a lighthouse 145 ft above sea level, the angle of depression of a boat 29°. How far is the boat from the lighthouse?
6. Rhombus
The rhombus has diagonal lengths of 4.2cm and 3.4cm. Calculate the length of the sides of the rhombus and its height
7. Lighthouse
The man, 180 cm tall, walks along the seafront directly to the lighthouse. The male shadow caused by the beacon light is initially 5.4 meters long. When the man approaches the lighthouse by 90 meters, its shadow shorter by 3 meters. How tall is the lightho
8. Diamond diagonals
Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square and the side length is 13 cm.
9. Hypotenuse - RT
A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle?
10. A bridge
A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. H
The angle of a straight road is approximately 12 degrees. Determine the percentage of this road.
12. Windbreak
A tree at a height of 3 meters broke in the windbreak. Its peak fell 4.5 m from the tree. How tall was the tree?
13. Two forces
The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F.
14. Garden fence
The garden has the shape of a rectangular triangle with an area of 96 square meters and a 16 m long one leg. How many meters of the fence need to be fenced?
15. Regular quadrangular pyramid
The height of the regular quadrangular pyramid is 6 cm, the length of the base is 4 cm. What is the angle between the ABV and BCV planes?
16. Isosceles
Isosceles trapezium ABCD ABC = 12 angle ABC = 40 ° b=6. Calculate the circumference and area.
17. ABCD square
In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment?
18. Angle of diagonal
Angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume.
19. Quarter circle
What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
20. Ratio of edges
The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.

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.