Planimetrics - math word problems - page 178 of 183
Number of problems found: 3656
- The tower
The observer sees the tower's base 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands? - Consumption 69174
The tower's roof has the shape of the shell of a rotating cone with a base diameter of 4.3 m. The deviation of the side from the plane of the base is 36°. Calculate the consumption of sheet metal to cover the roof, assuming 8% for waste. - Inaccessible 82710
Determine the distance between two inaccessible places K, L, if the angles KAL=62°10", LAB=41°23", KBL=66°34", and LBA were measured from points A, B, which are 870 m apart = 34°52". Thank you. - Maturitný - RR - base
In an isosceles triangle ABC with base AB, ∠BAC = 20°, AB = 4. The axis of the interior angle at vertex B intersects side AC at point P. Calculate the length of the segment AP. Give the result to two decimal places. - Rhombus
ABCD is a rhombus, ABD is an equilateral triangle, and AC is equal to 4. Find the area of the rhombus. - Cosine
Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and the hypotenuse 8.544. - Climb
The road has climbing 1:28. How big is the angle that corresponds to this climbing?
- See harmonics
Is it true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. The central segment crosses the intersection of the diagonals and is parallel to the bases. - Cablecar
Funicular on Petrin (Prague) was 408 meters long and overcame the difference of 106 meters in altitude. Calculate the angle of the climb. - Calculate roots of z
Calculate the ratio of the two fifth roots of the number 32. - Standing 22821
The heating plant sees the observer standing 26 m from the bottom of the chimney and seeing the top at an angle of 67 °. Thus, the chimney of the heating plant is how high? - Height difference
What height difference is overcome if we pass a road 1 km long with a pitch of 21 per mille? - Geodesist
Triangle-shaped field (triangle ABC) has a side AB = 129 m. path XY is parallel to the side AB, which divides triangle ABC into two parts with the same area. What will be the length of path XY? Help, please, geodesist. - Tunnel - quadrilateral
How long will the tunnel AB be, distances AD=35 m, DC=120 m, CB=85 m, and angles ADC=105 degrees and BCD=71 degrees. ABCD is a quadrilateral. - Mast angles and height
Calculate the height of the mast, whose foot can be seen at a depth angle of 11° and the top at a height angle of 28°. The mast is observed from a position 10 m above the level of the base of the mast.
- Decide 2
Decide whether points A[-2, -5], B[4, 3], and C[16, -1] lie on the same line - Traffic sign
There is a traffic sign for climbing on the road with an angle of 7%. Calculate at what angle the road rises (falls). - Difference 6029
Between the resorts is 15km, and the climb is 13 permille. What is the height difference? - Perimeter - ASA theorem
Calculate the perimeter of the triangle ABC if a = 12 cm, the angle beta is 38 degrees, and the gamma is 92 degrees. - Rectangle and squares
A 9cm × 15cm rectangle is divided into unit squares. How many paths are there from one rectangle vertex to the opposite vertex if one can only go to the right and up the sides of the squares?
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