Goniometry and trigonometry - math word problems - page 20 of 31
Number of problems found: 617
- View angle
At a distance of 10 m from the river bank, they measured the base AB = 50 m parallel to the bank. Point C on the other bank of the river is visible from point A at an angle of 32°30' and from point B at an angle of 42°15'. Calculate the width of the river - Area and two angles
Calculate the size of all sides and internal angles of a triangle ABC if it is given by area S = 501.9; and two interior angles α = 15°28' and β = 45°. - Airplane navigation
An airplane leaves an airport and flies west 120 miles and then 150 miles in the direction S 32.12°W. How far is the plane from the airport (round to the nearest mile)? - Mast
The mast has 16 a long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 9.7°. Determine the height of the mast if the sun above the horizon is at an angle 40°48'. - 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. - Unit circle
In the Cartesian coordinate system, a unit circle is given on which points A and B lie. Point O is the origin and has coordinates (0,0) and point B has coordinates (1,0). The size of angle BOA is 151°. Determine the x-coordinate of point A. - Crosswind
A plane is traveling 45 degrees N of E at 320 km/h when it comes across a current from S of E at 115 degrees of 20 km/h. What are the airplane's new course and speed?
- Space vectors 3D
The vectors u = (1; 3;- 4) and v = (0; 1; 1) are given. Find their sizes, calculate their angles, and determine the distances between them. - A man 7
A man wandering in the desert walks 3.8 miles in the direction of S 44° W. He then turns and walks 2.2 miles toward N 55° W. At that time, how far is he from his starting point? (Round your answer to two decimal places.) - A drone
A flying drone aimed the area for an architect. He took off perpendicularly from point C to point D. He was 300 m above ABC's plane. The drone from point D pointed at a BDC angle of 43°. Calculate the distance between points C and B in meters. - An observer
An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower? - Slope
What is the slope of a line with an inclination -325°? - Slope of track
Calculate the average slope (in permille and even in degrees) of the rail tracks between Prievidza (309 m AMSL) and Horná štubňa (624 m AMSL) if the track is 37 km long. - Goat and circles
What is the radius of a circle centered on the other circle, and is the intersection of the two circles equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which - Powerplant chimney
From the building window at the height of 7.5 m, we can see the top of the factory chimney at an altitude angle of 76° 30 ′. We can see the chimney base from the same place at a 5° 50 ′ depth angle. How tall is the chimney?
- Tunnel - quadrilateral
How long will the tunnel AB be, distances AD=35 m, DC=120 m, CB=85 m, and angles ADC=105 degrees and BCD=71 degrees. ABCD is a quadrilateral. - Road
Between cities, A and B is a route 9 km long of average 9‰ klesanie. Calculate the height difference between cities A and B. - Ratio in trapezium
The ratio of the height v and the base a, c in the trapezoid ABCD is 1:6:3. Its area is 324 square cm, and the peak angle B is 35 degrees. Determine the perimeter of the trapezoid. - Circular railway
The railway connects points A, B, and C in a circular arc, whose distances are | AB | = 30 km, AC = 95 km, and BC | = 70 km. How long will the track be from A to C? - Instantaneous 37201
The amplitude of the linear undamped harmonic oscillator is A = 12 cm, and the frequency f = 15 Hz. What is its instantaneous deflection at time a) t1 = 0.02s, b) t2 = 0.04s, when it was zero at time t = 0 s?
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Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.
