Planimetry - math word problems - page 168 of 187
Number of problems found: 3735
- Triangle ABC v2
The area of the triangle is 12 cm². Angle ACB = 30º , AC = (x + 2) cm, BC = x cm. Calculate the value of x. - View angle
From a tower 20 m high and 20 m away from a river, the width of the river appears to span an angle of 15°. How wide is the river at this location? - Mirror
The dimensions of a mirror are 750 mm × 700 mm, and the mirror is to be tilted 8° away from the wall. How many centimetres must the bottom of the mirror protrude from the wall? - In a right-angled 17
In right triangle DEF with hypotenuse f = 12 cm, the interior angle at vertex D is 60°. What is the length of side e? - Ropeway angle length
The ropeway climbs at an angle of 22°30'. Calculate its length if the height difference between the lower and upper station is 560 m. Sketch a picture - Depth angle
From a cliff of 150 meters high, we can see the ship at a depth angle of 9° at sea. How far is the ship from the cliff? - 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 °. - Rectangle
Calculate the length of the side HM and diagonal EM of rectangle EHMQ when given: |QM| = 29 cm and angle ∠ EHQ = 36 degrees. - Cable car
A cable car rises at an angle of 44° and connects the upper and lower stations with an altitude difference of 1089 m. How long is the continuous (endless) tow rope? - Triangle SAA
A triangle has one side of length 23 m and two interior angles of 60°. Calculate its perimeter and area. - Isosceles trapezoid
Find the height in an isosceles trapezoid if the area is 520 cm² and the base a = 25 cm and c = 14 cm. Calculate the interior angles of the trapezoid. - The right triangle
In the right triangle ABC with a right angle at C, we know the side lengths AC = 9 cm and BC = 7 cm. Calculate the length of the remaining side of the triangle and the size of all angles. - Triangles
Ivo wants to draw all the triangles whose two sides have a length of 4 cm and 9 cm, and the length of the third side is expressed in whole centimeters. How many triangles does he have? - Tower elevation angles
Find the height of the tower when the geodetic measured two angles of elevation α=34° 30'' and β=41°. The distance between places AB is 14 meters. - Plane flight distance
The plane flies at an altitude of 22.5 km to the observatory. At the time of the first measurement, it was seen at an elevation angle of 28° and during the second measurement at an elevation angle of 50°. Calculate the distance it flies between these two - Circumscribed circle ABC
Triangle ABC, with sides a = 15 cm, b = 17.4 cm, and c = 21.6 cm, is circumscribed by a circle. Calculate the area of the segments determined by the sides of the triangle. - Distance to Aircraft
The observer sees the plane at an elevation angle of 35° (angle from the horizontal plane). At that moment, the plane reported an altitude of 4 km. How far from the observer is the place over which the aircraft flies? They circled for hundreds of meters. - The ladder and wall
A 6.5-meter-long ladder rests against a vertical wall. Its lower end rests on the ground 1.6 meters from the wall. Determine how high the top of the ladder reaches and at what angle it rests against the wall. - Rectangle ABCD
The rectangle ABCD is given whose | AB | = 5 cm, | AC | = 8 cm, ∢ | CAB | = 30°. How long is the other side, and what is its area? - Area 4gon
Calculate the area of a parallelogram with two pairs of equal parallel sides of lengths 18 and 9, and interior angles of 45°, 135°,45°, 135°.
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