# Planimetrics - math word problems

Study plane measurements, including angles, distances, and areas. In other words - measurement and calculation of shapes in the plane. Perimeter and area of plane shapes.

1. Two forces The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F.
2. Is right-angled Can a triangle with the sides of sqrt 3, sqrt 5 and sqrt 8 (√3, √5 and √8) be a right triangle?
3. 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?
4. Clouds Approximately at what height is the cloud we see under an angle of 26°10' and see the Sun at an angle of 29°15' and the shade of the cloud is 92 meters away from us?
5. A square A square with length of diagonals 12cm give: a) Calculate the area of a square b) rhombus with the same area as the square, has one diagonal with length of 16 cm. Calculate the length of the other diagonal.
6. Diamond The diamond has a circumference of 48cm. Calculate the length of its side in dm.
7. Find the 5 Find the equation with center at (1,20) which touches the line 8x+5y-19=0
8. Diagonals at right angle In the trapezoid ABCD this is given: AB=12cm CD=4cm And diagonals crossed under a right angle. What is the area of this trapezoid ABCD?
9. Ratio of sides The triangle has a circumference of 21 cm and the length of its sides is in a ratio of 6: 5: 3. Find the length of the longest side of the triangle in cm. Miro stands under a tree and watching its shadow and shadow of the tree. Miro is 180 cm tall and its shade is 1.5 m long. The shadow of the tree is three times as long as Miro's shadow. How tall is the tree in meters?
11. Prove Prove that k1 and k2 is the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x2+y2+2x+4y+1=0 k2: x2+y2-8x+6y+9=0
12. Display case Place a glass shelf at the height of 1m from the bottom of the display case in the cabinet. How long platter will we place at this height? The display case is a rectangular triangle with 2 m and 2.5 m legs.
13. Thales Thales is 1 m from the hole. The eyes are 150 cm above the ground and look into the hole with a diameter of 120 cm as shown. Calculate the depth of the hole.
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? Shade the area on the grid that shows 5/8 x 2/4
16. Vector 7 Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
17. Decagon Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m
18. Two people Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walking at the rate of 4 kph in one road, Jenelyn walking at the rate of 8 kph on the other road. How long will it take for them to be 20√5 km apar
19. Image reduction To say that I am mathematically challenged is a gross understatement! I'm trying to help my friend determine how to calculate percentages of reduction or enlargement for a quilt pattern. She is creating a drawing of a cute picture which will become a pie
20. Hamster cage Ryan keeps his hamster cage on his dresser. The area of the top of Ryan's dresser is 1 2\3 as large as the area of the bottom of his hamster cage. The area of the dresser top is 960 square inches. How many square inches of his dresser top are not covered b

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