Planimetrics - math word problems - page 153 of 170
Study plane measurements, including angles, distances, and areas. In other words - measurement and calculation of shapes in the plane. Perimeter and area of plane shapes.Number of problems found: 3396
- Calculate triangle
In the triangle, ABC, calculate the sizes of all heights, angles, perimeters, and area if given a=40cm, b=57cm, and c=59cm. - 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 airplane
The airplane sights a runway at an angle of depression of 23°. It is flying at an altitude of 3 kilometers above the ground. What is the horizontal distance of the airplane from the airport? - An angle of depression
The lighthouse sees a ship at an angle of depression of 25°. The observer from the lighthouse is 82 m above sea level. How far is the ship from the top of the lighthouse?
- A trapezoid
A trapezoid with a base length of a = 36.6 cm, with angles α = 60°, β = 48°, and the height of the trapezoid is 20 cm. Calculate the lengths of the other sides of the trapezoid. - 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? - Equilateral triangle
How long should the minimum radius of the circular plate be cut into an equilateral triangle with side 21 cm from it? - Aircraft
From the aircraft flying at an altitude of 500m, they observed places A and B (at the same altitude) in the direction of flight at depth angles alpha = 48° and beta = 35°. What is the distance between places A and B? - Horizontal 83362
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.
- Pentadecagon
Calculate the area of a regular 15-sides polygon inscribed in a circle with a radius r = 4. Express the result to two decimal places. - Right angle
In a right triangle ABC with a right angle at the apex C, we know the side length AB = 24 cm and the angle at the vertex B = 71°. Calculate the length of the legs of the triangle. - TV tower
Calculate the height of the television tower if an observer standing 430 m from the base of the tower sees the peak at an altitude angle of 23°. - Triangle ABC v2
The area of the triangle is 12 cm square. Angle ACB = 30º , AC = (x + 2) cm, BC = x cm. Calculate the value of x. - Pentagon
Calculate the length of a regular pentagon's side, circumference, and area, inscribed in a circle with a radius r = 6 cm.
- Calculate 83356
The distance of the chord from the center is 6 cm. The central angle is 60°. Calculate the area of the circular segment. - Circumference 26361
The ABCD diamond has a circumference of 72 cm. The longer diagonal of the animal with the line segment AB angle is 30 °. Calculate the area of the ABCD diamond. - Calculate 43331
From the lookout tower, 70 meters high, we see a man at a depth angle of 15 degrees. Calculate how far one stands from the base of the lookout tower. Draw and calculate. - Circumscribed 22713
Calculate the circumference and the area of a regular ten-angle polygon if the radius of the circumscribed circle r = 20 cm. - Distance 19043
Radar sees an aircraft at an altitude angle of 15°24', and the direct distance from the radar is 5545 m. At what altitude does the aircraft fly?
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