# Triangle + right triangle - math problems

1. The right triangle In the right triangle ABC with right angle at C we know the side lengths AC = 9 cm and BC = 7 cm. Calculate the length of the remaining side of the triangle and the size of all angles.
2. Isosceles triangle Calculate the size of the interior angles and the length of the base of the isosceles triangle if the length of the arm is 17 cm and the height to the base is 12 cm.
3. TV tower Calculate the height of the television tower if an observer standing 430 m from the base of the tower sees the peak at an altitude angle of 23°? The ladder touch on a wall at a height of 7.5 m. The angle of the inclination of the ladder is 76°. How far is the lower end of the ladder from the wall?
5. Telegraph poles The bases of two adjacent telegraph poles have a height difference of 10.5 m. How long do the wires connect the two poles if the slope is 39° 30´?
6. Diamond area from diagonals In the diamond ABCD is AB = 4 dm and the length of the diagonal is 6.4 dm long. What is the area of the diamond?
7. Height of pyramid The pyramid ABCDV has edge lengths: AB = 4, AV = 7. What is its height?
8. Circle and square An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD.
9. Observation tower From the observation tower at a height of 105 m above sea level, the ship is aimed at a depth angle of 1° 49´. How far is the ship from the base of the tower?
10. Triangular prism Calculate the surface of a regular triangular prism, the edges of the base are 6 cm long and the height of the prism is 15 cm.
11. Probability How probable is a randomly selected three-digit number divisible by five or seven?
12. The right triangle The right triangle ABC has a leg a = 36 cm and an area S = 540 cm2. Calculate the length of the leg b and the median t2 to side b.
13. Concentric circles and chord In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius have the concentric circle while touch this chord?
14. Flakes A circle was described on the square, and a semicircle above each side of the square was described. This created 4 "flakes". Which is bigger: the content of the central square or the content of four chips?
15. The bases The bases of the isosceles trapezoid ABCD have lengths of 10 cm and 6 cm. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and content of the ABCD trapezoid.
16. Annulus from triangle Calculate the content of the area bounded by a circle circumscribed and a circle inscribed by a triangle with sides a = 25mm, b = 29mm, c = 36mm
17. The conical The conical candle has a base diameter of 20 cm and a side of 30 cm. How much dm ^ 3 of wax was needed to make it?
18. Cone roof How many m2 of roofing is needed to cover a cone-shaped roof with a diameter of 10 m and a height of 4 m? Add an extra 4% to the overlays.
19. Spherical cap The spherical cap has a base radius of 8 cm and a height of 5 cm. Calculate the radius of a sphere of which this spherical cap is cut.
20. The rescue helicopter The rescue helicopter is above the landing site at a height of 180m. The site of the rescue operation can be seen from here at a depth angle of 52° 40 '. How far will the helicopter land from the rescue site?

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