Planimetry - math word problems - page 67 of 72
Number of problems found: 1438
- Wall and ladder
A ladder leans against a wall, reaching a height of 6.5 m. How long is the ladder if it makes an angle of 60° with the horizontal floor? - Triangle 75
Triangle ABC has angle C bisected and intersected AB at D. Angle A measures 20 degrees, and angle B measures 40 degrees. The question is to determine AB-AC if length AD=1. - 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? - An isosceles trapezoid
An isosceles trapezoid has base angles of 50° each, and its bases are 20 cm and 30 cm. Compute its area. - Parallelogram - two sides
The parallelogram has the sides a = 25.3 b = 13.8, and the angle closed by the sides is a = 72°. Calculate the area of the parallelogram. - Tower distance
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. - Jewel
A rhombus-shaped jewel has an area of 23 mm² and a side length of 5.9 mm. Calculate the size of the acute angle of the rhombus. - Circumscribed circle
In triangle ABC, we know a = 4 cm, b = 6 cm, γ = 60°. Calculate the area and radius of the inscribed and circumscribed circle. - Aircraft
From the aircraft flying at an altitude of 500 m, 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? - Triangle height angle
Calculate the lengths of the sides in an isosceles triangle, given the height (to the base) Vc= 8.8 cm and the angle at the base alpha= 38°40`. - Three surveyors
Three surveyors are tasked with measuring the height of a mast standing on a flat plain. The first surveyor, standing 100 m from the mast, measured the elevation angle α; the second, standing 200 m from the mast, measured the elevation angle β; and the th - Sun and shadow
The pole is stuck vertically into the ground. The protruding length is 1 m. What is the length of the shadow cast when the sun is just 50° above the horizon? - Heptagon perimeter
Calculate a regular heptagon's perimeter if its shortest diagonal length is u=14.5 cm. - 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)? - Decadal - flower bed
The castle park includes a flower bed in the shape of a regular decagon with an area of 432.8 m². Determine the distance between adjacent vertices of the flower bed. - The chord - angle
The distance of the chord from the center is 6 cm. The central angle is 60°. Calculate the area of the circular segment. - What is 19
What is the length of the hypotenuse c of right triangle ABC if the angle α at vertex A is 30° and leg a = 3 cm? - Big tree
You are standing 20 feet away from a tree, and you measure the elevation angle to be 38°. How tall is the tree? - Triangle angle sides
In the right triangle ABC, calculate the magnitude of the interior angles if / AB / = 13 cm; / BC / = 12 cm and / AC / = 5 cm.
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