Planimetrics - math word problems - page 168 of 183
Number of problems found: 3656
- The staircase
The staircase has a total height of 3.6 m and forms an angle of 26° with the horizontal. Calculate the length of the whole staircase. - Inscribed and described circle
Find the radii of a circle inscribed and circumscribed by a regular pentagon whose side measures 3 cm. - Isosceles 4741
The arm is five times longer than its base in an isosceles triangle. Calculate its interior angles. - Described 7872
In the KLM isosceles triangle, the KL base is 24 cm long, and the arm measures 15 cm. What is the radius of the circle described by this triangle? - Decagon 5145
Find the area of a regular decagon if its side is 10 cm in size. - Bearing - navigation
A ship travels 84 km on a bearing of 17° and then travels on a bearing of 107° for 135 km. Find the distance of the end of the trip from the starting point to the nearest kilometer. - 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.
- The ladder - RT
The ladder 16 feet reaches up 14 feet on a house wall. The 90-degree angle at the base of the house and wall. What are the other two angles or the length of the leg of the yard? - The Eiffel Tower
The top of the Eiffel Tower is seen from 600 meters at a 30 degree angle. Find the tower's height. - Construct 13581
The vertices of the triangle ABC lie on the circle k. The circle k is divided into three parts in a ratio of 1:2:3. Construct this triangle. - A chord
In a circle radius of 6 cm, a chord is drawn 3 cm from the center. Calculate the angle subtended by the chord at the center of the circle. Hence find the length of the minor arc cut off by the chord. - A dodecagon
Find the surface area of a regular 12-sided polygon if its side is a = 12 cm. - 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? - Observation 76644
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? - Divide an isosceles triangle
How can an isosceles triangle be divided into two parts with equal areas perpendicular to the axis of symmetry (into a trapezoid and a triangle)?
- Diagonals of the rhombus
How long are the diagonals e, and f in the diamond if its side is 5 cm long and its area is 20 cm²? - Greatest angle
Calculate the greatest triangle angle with sides 124, 323, 302. - 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 - Rhomboid
The rhomboid sides' dimensions are a= |AB|=5cm, b = |BC|=6 cm, and the angle's size at vertex A is 60°. What is the length of the diagonal AC? - De Moivre's formula
There are two distinct complex numbers, such that z³ is equal to 1 and z is not equal to 1. Calculate the sum of these two numbers.
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