Planimetry - math word problems - page 65 of 72
Number of problems found: 1438
- Three pillars
On a straight road, three pillars are 6 m high at the same distance of 10 m. At what angle of view does Walter see each pillar if it is 30 m from the first and his eyes are 1.8 m high? - Parallelogram - sides L
In a parallelogram, the sum of the lengths of the sides a+b = 234. The angle subtended by the sides a and b is 60°. The diagonal size against the given angle of 60° is u=162. Calculate the sides of the parallelogram, its perimeter, and its area. - Binibini
Binibini owns a triangular residential lot bounded by two roads intersecting at 70°. The sides of the lot along the road are 62 m and 43 m, respectively. Find the length of the fence needed to enclose the lot. (express answers to the nearest hundredths) - Colored area
How large is the area colored brown inside a square of side 6 cm if each of the four brown circular segments is from a circle with a radius of the length of the square's side? The length of the circular segments is equal to the length of the side of the s - River bank distance
Adam (A) stands on one river bank, and Bedrich (B) stands on the other. To determine their distance, the base AC with a length of 136 m and the angles CAB with a size of 70°21' and ACB with a size of 43°44' were measured on one river bank. What is the dis - Triangle tangent area
In the triangle ABC, b=5 cm, c=6 cm, /BAC/ = 80° are given. Calculate the sizes of the other sides and angles, and further determine the sizes of the tangent tc and the area of the triangle. - A construction
A construction worker is trying to find the height of a skyrise building. He is standing some distance away from the base with an elevation angle of 65 degrees. The worker moves 50 feet closer and measures the angle of elevation to be 75 degrees. Find the - Parallelogram diagonals
Find the area of a parallelogram if the diagonals u1 = 15 cm and u2 = 12 cm and the angle formed by them is 30 degrees. - Tower distance
How far from the lookout tower, 48 m high, did the tourist stand if he saw its top at an angle of 40°? - Tower distance angle
From the smaller observation tower, we see the top of the larger tower at an elevation angle of 23°, and the difference in their heights is 12 m. How far apart are the observation towers? - Cable car climb
The lower station of the cable car in Smokovec is at an altitude of 1025 m, and the upper station at Hrebienk is at an altitude of 1272 m. Calculate the climb of the cable car if the horizontal distance between the slopes is 1921 m. - Parallelogram diagonal construction
Construct a parallelogram ABCD if a=5 cm, height to side a is 5 cm, and angle ASB = 120 degrees. S is the intersection of the diagonals. - 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? - 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. - 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? - 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. - 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. - 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) - 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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