# Right triangle - examples - page 17

1. Chimney Lower circumference of of the chimney is 12.57 m, top circumference is 5.655 m. The slope of the walls is 87°. Determine the height of the chimney.
2. Perimeter of triangle In triangle ABC angle A is 60° angle B is 90° side size c is 15 cm. Calculate the triangle circumference.
3. Right triangle trigonometrics Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
4. ABS CN Calculate the absolute value of complex number -15-29i.
5. Hexa prism Determine the volume of hex prism with edge base 4 cm. The body height is 28 cm.
6. Area of RT 2 Calculate the area of right triangle whose legs have a length 5.8 cm and 5.8 cm.
7. Circle inscribed Calculate the perimeter and area of a circle inscribed in a triangle measuring 3 , 4 and 5 cm.
8. Catheti The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs.
9. Is right triangle One angle of the triangle is 36° and the remaining two are in the ratio 3:5. Determine whether triangle is a rectangular triangle.
10. Rectangular trapezium Calculate the perimeter of a rectangular trapezium when its content area is 576 cm2 and sice a (base) is 30 cm, height 24 cm.
11. RTriangle 17 The hypotenuse of a right triangle is 17 cm. If you decrease both two legs by 3 cm you will reduce the hypotenuse by 4 cm. Determine the length of this legs.
12. Right angled From the right triangle with legs 12 cm and 20 cm we built a square with the same content as the triangle. How long will be side of the square?
13. Rotating cone Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm.
14. Perimeter of circle Calculate the circumference of described circle to the triangle with sides 9,12,15 cm.
15. Inscribed circle Write the equation of a incircle of the triangle KLM if K [2,1], L [6,4], M [6,1].
16. The field The player crossed the field diagonally and walked the length of 250 m. Calculate the length of the field, circumference if one side of field 25 meters.
17. Obtuse angle The line OH is the height of the triangle DOM, line MN is the bisector of angle DMO. obtuse angle between the lines MN and OH is four times larger than the angle DMN. What size is the angle DMO? (see attached image)
18. Square circles Calculate the length of the described and inscribed circle to the square ABCD with a side of 5cm.
19. Rhombus One angle of a rhombus is 136° and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus.
20. Hexagon rotation A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated?

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