Planimetrics - math word problems - page 164 of 185
Number of problems found: 3687
- 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. - 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 36m, 21m long, and the remaining sides are 14m, 16m long. Determine the size of the interior angles with a longer base. - Triangle's centroid
In the triangle ABC the given lengths of its medians tc = 9, ta = 6. Let T be the intersection of the medians (triangle's centroid), and the point S is the center of the side BC. The magnitude of the CTS angle is 60°. Calculate the length of the BC side t - Parallelogram
The sides of the parallelogram are 8 cm and 6 cm long, and the diagonals' angle is 60°. What is its area? - 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. - Rhombus area
Calculate the area and height of the rhombic cover plate to which the following applies: d (BC) = 60 cm, angle BAD = 45 °, angle ADB = 90 °. - Maggie
Maggie observes a car and a tree from a window. The angle of depression of the car is 45 degrees, and that of the tree is 30 degrees. If the distance between the vehicle and the tree is 100 m, find Maggie's distance from the tree. - Right triangle
Calculate the length of the remaining two sides and the angles in the rectangular triangle ABC if a = 10 cm, angle alpha = 18°40'. - Right angled triangle 3
Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees. Find the length of its unknown sides. - The mast
A 40 m high mast is secured in half by eight ropes 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance. - How far
From the top of a lighthouse 145 ft above sea level, the angle of depression of a boat is 29°. How far is the boat from the lighthouse? - Triangle
Calculate the area of the triangle ABC if b = c = 17 cm, R = 19 cm (R is the circumradius). - Triangle SAA
The triangle has one side long 23 m, and its two internal angles are 60°. Calculate the perimeter and area of the triangle. - 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| = 57m, 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 of - 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’? - The tower
From a window 8 m above the horizontal plane, we can see the top of the tower at an elevation angle of 53 degrees 20 minutes, and its base at an angle of 14 degrees 15 minutes. How high is the tower?
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