Planimetrics - math word problems - page 166 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: 3400
- Clouds
We see the cloud under an angle of 26°10' and the Sun at an angle of 29°15'. The shade of the cloud is 92 meters away from us. Approximately at what height is the cloud? - See harmonics
Is it true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. The central segment crosses the intersection of the diagonals and is parallel to the bases. - Isosceles 7661
The area of the isosceles triangle is 8 cm2, and its arm's length is 4 cm. Calculate the sizes of its interior angles. - Triangle in circle
Vertices of the triangle ABC lies on a circle with radius 3 so that it is divided into three parts in the ratio 4:4:4. Calculate the circumference of the triangle ABC.
- Depth angles
At the top of the mountain stands a castle with a tower 30 meters high. We see the crossroad at a depth angle of 32°50' and the heel at 30°10' from the top of the tower. How high is the top of the mountain above the crossroad? - Right triangle eq2
Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70. - Measurements of a triangle
Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. A = 50°, b = 30 ft, c = 14 ft - A hiker
A hiker plans to hike up one side of a mountain and down the other side of points a mountain, each side of the mountain formed by a straight line. The angle of elevation at the starting point is 42.4 degrees, and the angle of elevation at the end is 48.3 - Parametrically 6400
Find the angle of the line, which is determined parametrically x = 5 + t y = 1 + 3t z = -2t t belongs to R and the plane, which is determined by the general equation 2x-y + 3z-4 = 0.
- Wheel gear
A drive wheel of radius two is connected to a drive wheel of radius one by a pulley of length 17. What is the distance between the wheel axles? - Ratio iso triangle
The ratio of the sides of an isosceles triangle is 7:6:7. Find the base angle to the nearest answer correct to 3 significant figures. - Four sides of trapezoid
In the trapezoid ABCD is |AB| = 73.6 mm; |BC| = 57 mm; |CD| = 60 mm; |AD| = 58.6 mm. Calculate the size of its interior angles. - Space vectors 3D
The vectors u = (1; 3; -4), v = (0; 1; 1) are given. Find the size of these vectors, calculate the angle of the vectors, and the distance between the vectors. - Cosine
Cosine and sine theorem: Calculate all missing values (sides and angles) of the triangle ABC. a = 20 cm; b = 15 cm; γ = 90°; c =? cm; α =? °; β =? °
- Simple right triangle
Right triangle. Given: side c = 18.8 and angle beta = 22° 23'. Calculate sides a, b, angle alpha, and area. - Length of the chord
Calculate the length of the chord in a circle with a radius of 25 cm with a central angle of 26°. - Complex roots
Find the sum of the fourth square root of the number 16. - Trapezoid IV
In a trapezoid ABCD (AB||CD) is |AB| = 15cm |CD| = 7 cm, |AC| = 12 cm, AC is perpendicular to BC. What area has a trapezoid ABCD? - Airplane navigation
An airplane leaves an airport and flies west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?
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