Right triangle - math word problems

1. Vertices of RT
Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle.
Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles.
3. Forces on earth directions
A force of 60 N [North] and 80 N [East] is exerted on an object wigth 10 kg. What is the acceleration of the object?
4. Tree
Between points A and B is 50m. From A we see a tree at an angle 18°. From point B we see the tree in three times bigger angle. How tall is a tree?
5. 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)
6. 30-gon
At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
7. V-belt
Calculate a length of the V-belt when the diameter of the pulleys is: D1 = 600 mm D2 = 120 mm d = 480 mm
8. Center of gravity
In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT.
9. Cube in sphere
The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
10. Sun rays
If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current he
11. Isosceles right triangle
Contents of an isosceles right triangle is 18 dm2. Calculate the length of its base.
12. Diagonals
Draw a square ABCD whose diagonals have a length of 6 cm
13. Equilateral triangle
The equilateral triangle has a 23 cm long side. Calculate its content area.
The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?
15. Isosceles triangle
Calculate area and perimeter of an isosceles triangle ABC with base AB if a = 6 cm, c = 7 cm.
16. Square
Calculate the perimeter and the area of square with a diagonal length 30 cm.
17. Billboard
Rectangular billboard is 2.5 m long with a diagonal 2.8 m long. Calculate the perimeter and the content area of the billboard.
18. Land - isosceles trapezoid
Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m.
19. Diagonals of diamond
Find the area and circumference of the diamond ABCD with 15m and 11m diagonals.
20. Two aircraft
From the airport will start simultaneously two planes, which fly tracks are perpendicular to each other. The first flying speed of 680 km/h and the second 840 km/h. Calculate how far the aircraft will fly for half an hour.

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