# Goniometry and trigonometry - math word problems

#### Number of problems found: 423

- Heptagonal pyramid

A hardwood for a column is in the form of a frustum of a regular heptagonal pyramid. The lower base edge is 18 cm, and the upper base of 14 cm. The altitude is 30 cm. Determine the weight in kg if the wood density is 10 grams/cm^{3}. - Goat and circles

What is the radius of a circle centered on the other circle and the intersection of the two circles is 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 g - Gears

The front gear on the bike has 32 teeth and the rear, on the wheel, has 12 teeth. How many times does the bike's rear-wheel turn if you turn the right pedal 30 times? What distance will you go if the circumference of the bicycle wheel is 250 cm? - Book reading

If we read the book at a speed of 15 pages a day, we read it 3 days before we read it at a speed of 10 pages per day. If I read at 6 pages per day, how many days will I read the book? - Collecting

For the first week of material collection events are picked up at the school 850 kg of paper and 305 kg of rags which represented 55% of total collection for 14 days. How many kilograms of secondary raw materials were handed over totally? - Shooter

The shooter fired at a target from a distance 11 m. The individual concentric circle of targets has radius increments of 1 cm (25 points) by 1 point. The shot was shifted by 8' (angle degree minutes). How many points should win his shot? - Five inlets

The tank can be filled with five equally powerful inlets. If the tank is filled by four of these inlets, it takes a total of 30 minutes to fill one-third of the tank. How many minutes does it take to fill an empty tank if it is filled with all five inlets - Slope of the pool

Calculate slope (rise:run) of the bottom of the swimming pool long 30 m. Water depth at beginning of the pool is 1.13 m (for children) and depth at the end is 1.84 m (for swimmers). Slope express as percentage and as the angle in degrees. - Segment in a triangle

In a triangle ABC with the side/AB/ = 24 cm is constructed middle segment/DE/ = 18 cm parallel to the side AB at a distance 1 cm from AB. Calculate the height of the triangle ABC to side AB. - Two forces

The two forces F1 = 580N and F2 = 630N, have an angle of 59 degrees. Calculate their resultant force, F. - Black diamond run

Taleah is skiing down a black diamond run. She begins skiing at the top of a ski trail whose elevation is about 8625 feet. The ski run ends toward the base of the mountain at 3800 feet. The horizontal distance between these two points is about 4775 feet. - Altitude angles

Cities A, B, C lie in one elevation plane. C is 50 km east of B, B is north of A. C is deviated by 50° from A. The plane flies around places A, B, C at the same altitude. When the aircraft is flying around B, its altitude angle to A is 12°. Find the altit - Cylinder

The cylinder-shaped container has 80 liters of water. The water reaches 45 cm height. How many water liters will be in a container if the water level extends to a height of 72 cm? Write the result in liters, write down only as a whole or decimal number. - 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 depth angle of 5° 50 ′. How tall is the chimney? - Quadrilateral oblique prism

What is the volume of a quadrilateral oblique prism with base edges of length a = 1m, b = 1.1m, c = 1.2m, d = 0.7m, if a side edge of length h = 3.9m has a deviation from the base of 20° 35' and the edges a, b form an angle of 50.5°. - Water channel

The cross section of the water channel is a trapezoid. The width of the bottom is 19.7 m, the water surface width is 28.5 m, the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flo - Nonagon

Calculate the area and perimeter of a regular nonagon if its radius of the inscribed circle is r = 10cm - The body

The body slides down an inclined plane forming an angle α = π / 4 = 45° under the action of a horizontal plane under the effect of friction forces with acceleration a = 2.4 m/s ^ 2. At what angle β must the plane be inclined so that the body slides on it - Sun rays

If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current heig - Sugar production

From 1 ton of beet, 150 kg of sugar is produced. To clean 1 ton of sugar, 450 kg of lime is consumed. Calculate how many kgs of lime is consumed when processing 1 ton of sugar beet?

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