Planimetry - math word problems - page 166 of 187
Number of problems found: 3735
- Length 26
The length of the median of a trapezoid is 10 inches. The median divides the trapezoid into two regions whose areas are in the ratio 3:5. What is the length of the shorter base? - Central angle
A circle k with a center at point S and a radius of 6 cm is given. Calculate the size of the central angle subtended by a chord 10 cm long. - Elevation angle
An airliner currently flying over a location 2,400 m away from the observer's location is seen at an elevation angle of 26° 20'. At what height does the plane fly? - V-belt
Calculate the length of a belt running on two pulleys with diameters of 105 mm and 393 mm, with a centre-to-centre distance of 697 mm. - Steeple
A church tower is seen from the road at an elevation angle of 52°. When we move back a further 29 metres, it is seen at an elevation angle of 21°. How tall is the tower? - Subtracting complex in polar
Given w =√2(cosine (pi/4) + i sine (pi/4) ) and z = 2 (cosine (pi/2) + i sine (pi/2) ). What is w - z expressed in polar form? - Land scale drawing
The land has a triangle shape with sides of 300 m, 200 m, and 245 m. Draw it on a scale of 1:5,000. - Kite deltoid angles
A paper kite is shaped like a deltoid ABCD, with two shorter sides 30 cm long, two longer sides 51 cm long, and a shorter diagonal 48 cm long. Determine the sizes of the internal angles of the given deltoid. - Trapezoid interior angles
The area for shooting training has the shape of a trapezoid, the parallel sides of which are 36 m, 21 m long, and the remaining sides are 14 m, 16 m long. Determine the size of the interior angles with a longer base. - A trapezoid
A trapezoid has a base length of a = 36.6 cm, with angles α = 60°, β = 48°, and a height of 20 cm. Calculate the lengths of the other sides of the trapezoid. - Church tower
Archdeacon church in Usti nad Labem has diverted the tower by 186 cm. The tower is 65 m high. Calculate the angle by which the tower is tilted. Results are written in degree minutes. - EQL triangle
Calculate the inradius and circumradius of an equilateral triangle with side a=67 cm. - Lengths of medians from coordinates
There is a triangle ABC: A [-6.6; 1.2], B [3.4; -5.6], C [2.8; 4.2]. Calculate the lengths of its medians. - Intersection of the altitudes
In the acute triangle KLM, the angle KLM is 68°. Point V is the intersection of the altitudes, and P is the foot of the altitude on the side LM. The angle P V M axis is parallel to the side KM. Compare the sizes of angles MKL and LMK. - In trapezoid 3
In trapezoid ABCD, the following elements are given: lengths of the parallel sides a = 20 cm and c = 11 cm, angle α = 63°36', and angle β = 79°36'. Calculate the lengths of the other two sides and the sizes of the remaining angles. - Parallelogram - area
Calculate the area of the parallelogram if the sides are a = 80, b = 60 long, and the size of the diagonal angle is 60°. - Angles of elevation
From points A and B on level ground, the angles of elevation of the top of a building are 25° and 37°, respectively. If |AB| = 57 m, calculate, to the nearest meter, the distances of the top of the building from A and B if they are both on the same side o - Loonie
Loonie has three wooden sticks measuring 17 inches, 21 inches, and 25 inches. He lays them down to form a triangle. Find the measure of the angle enclosed by 17 inches and 21 inches. (Express answers to the nearest hundredths) (using the law of cosines) - 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’? - Landing strip
How long is the runway at an airport if, at an altitude of 1.2 km, the beginning of the runway is visible at a depression angle of 58° and the end at a depression angle of 27°?
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