Goniometry and trigonometry - math word problems - page 12 of 32
Number of problems found: 634
- Cable Car Path Length
The cable car rose at an angle of 15 °. The height difference between the upper and lower stations is 106 m. Calculate the path's length. - Chimney - view angle
From a distance of 36 meters from the chimney base, its top can be seen at an angle of 53°. Calculate the chimney height and the result round to whole decimeters. - 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 - 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°. - Central angle calculation
There is a circle with a radius of 10 cm and its chord, which is 12 cm long. Calculate the magnitude of the central angle that belongs to this chord. - Roof angle
The house's roof has the shape of an isosceles triangle with arms 4 m long and the size of the base 6 m. How big an angle alpha does its roof make? - Stick shadow angle
The meter stick is located on the meridian plane and deviated from the horizontal plane to the north by an angle of magnitude 70°. Calculate the length of the shadow cast by a meter stick at true noon if the Sun culminates at an angle of 41°03'. - 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. - Parallelogram
Find the parallelogram's perimeter, where base a = 8 cm, height v = 3 cm, and angle alpha = 35° is the magnitude of the angle at vertex A. - Children playground
The playground has a trapezoid shape, and the parallel sides have a length of 36 m and 21 m. The remaining two sides are 14 m long and 16 m long. Find the size of the inner trapezoid angles. - The pond
We can see the pond at an angle of 65°37'. Its endpoints are 155 m and 177 m away from the observer. What is the width of the pond? - Tree
Between points A and B is 50 m. From A, we see a tree at an angle of 18°. From point B, we see the tree at a three times bigger angle. How tall is a tree? - Right triangle
It is given a right triangle angle alpha of 90 degrees the beta angle of 55 degrees c = 10 cm use the Pythagorean theorem to calculate sides a and b - In the desert
A man wondering in the desert walks 5.7 miles in the direction S 26° W. He then turns 90° and walks 9 miles in the direction N 49° W. At that time, how far is he from his starting point, and what is his bearing from his starting point? - ABS, ARG, CONJ, RECIPROCAL
Let z=-√2-√2i where i2 = -1. Find |z|, arg(z), z* (where * indicates the complex conjugate), and (1/z). Where appropriate, write your answers in the form a + i b, where both a and b are real numbers. Indicate the positions of z, z*, and (1/z) on an Argand - A rhombus 4
A rhombus has a side length of 10 cm. Find the angles at each vertex of the rhombus if the shorter diagonal measures 7 cm. Give your answers to the nearest degree and provide clear geometric reasoning at each step. - Distance Between Boats
An observer watches two boats at depth angles of 64° and 48° from the top of the hill, which is 75 m above the lake level. Determine the distance between the boats if both boats and the observer are in the same vertical plane. - Diamond height angle
What is the height of a diamond with a side 6 cm long if the angle formed by the sides is 78 degrees and 10 '? - View angle - river
The 15 m high building is 30 m away from the river bank. The river's width can be seen from the roof of this building at an angle of 15°. How wide is the river?
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