# Right triangle - 9th grade (14y) - examples - page 12

1. 3d vector component The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?
2. Circle tangent It is given to a circle with the center S and radius 3.5 cm. Distance from the center to line p is 6 cm. Construct a circle tangent n which is perpendicular to the line p.
3. Diagonal 20 Diagonal pathway for the rectangular town plaza whose length is 20 m longer than the width. if the pathway is 20 m shorter than twice the width. How long should the pathway be?
4. Vertices of RT Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle.
5. RT leg and perimeter Calculate the length of the sides of a right triangle ABC with hypotenuse c when the length of a leg a= 84 and perimeter of the triangle o = 269.
6. Lamp cone Calculate the surface of a lamp shade shaped of a rotary truncated cone with base diameter 32 cm and 12 cm and height 24 cm.
7. Median In triangle ABC is given side a=10 cm and median ta= 13 cm and angle gamma 90°. Calculate length of the median tb.
8. Cosine The point (8, 6) is on the terminal side of angle θ. cos θ = ?
9. Tree How tall is the tree that observed in the visual angle of 52°? If I stand 5 m from the tree and eyes are two meters above the ground.
10. Rhombus ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus. In the square ABCD point P is in the middle of the DC side and point Q in the middle pages AD. If the area of quadrilateral BQPC is 49 cm2, what is the area of ABCD?
12. Right triangle Right triangle ABC with side a = 19 and the area S = 95. Calculate the length of the remaining sides.
13. Tent Calculate how many liters of air will fit in the tent that has a shield in the shape of an isosceles right triangle with legs r = 3 m long the height = 1.5 m and a side length d = 5 m.
14. Thales Calculate the length of the Thales' circle described to right triangle with hypotenuse 18.4 cm.
15. Chord MN Chord MN of circle has distance from the center circle S 120 cm. Angle MSN is 64°. Determine the radius of the circle.
16. Hexagonal pyramid Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.
17. Rectangular trapezoid Calculate the content of a rectangular trapezoid with a right angle at the point A and if |AC| = 4 cm, |BC| = 3 cm and the diagonal AC is perpendicular to the side BC.
18. Pyramid in cube In a cube with edge 12 dm long we have inscribed pyramid with the apex at the center of the upper wall of the cube. Calculate the volume and surface area of the pyramid.
19. Right angled triangle 2 LMN is a right angled triangle with vertices at L(1,3), M(3,5) and N(6,n). Given angle LMN is 90° find n
20. Sails We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail?

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.