# Goniomentry and trigonometry - math word problems

#### Number of problems found: 391

• The right triangle In the right triangle ABC with right angle at C we know the side lengths AC = 9 cm and BC = 7 cm. Calculate the length of the remaining side of the triangle and the size of all angles.
• Find the Find the content of a regular 12 sided polygon, if its side a = 12 cm.
• Inclined plane The body stays on an inclined plane and exerts a compressive force of 70N on it. Find the angle between the inclined plane and the horizontal if a gravitational force of 100N acts on the body.
• Triangle in a square In a square ABCD with side a = 6 cm, point E is the center of side AB and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides.
• Six workers Six workers earned a total of CZK 12,600 per week on the construction site (5 working days). How much do 7 workers earn in 10 days with the same daily average salary?
• Tangents to ellipse Find the magnitude of the angle at which the ellipse x2 + 5 y2 = 5 is visible from the point P[5, 1] .
• Cook on gas The gas cylinder will last for 30 weekends for 2 hours of daily cooking. How many days will we be able to cook on a new cylinder when we cook 3 hours a day?
• Lookout tower Calculate the height of a lookout tower forming a shadow of 36 m if at the same time a column 2.5 m high has a shadow of 1.5 m.
• Gears The front gear on the bike has 32 teeth and the rear, on the wheel, has 12 teeth. How many times does the rear wheel of the bike turns if you turn the right pedal 30 times? What distance will you go if the circumference of the bicycle wheel is 250 cm?
• Mother and daughter Mother is 44 years old, her daughter 14. How many years ago was her mother four times older than her daughter?
• Angle of cone The cone has a base diameter of 1.5 m. The angle at the main apex of the axial section is 86°. Calculate the volume of the cone.
• Lumberjacks Fifteen lumberjacks would take 12 days to destroy the broken trees. How many days would this work require if 5 workers added to it after 4 days?
• Inscribed and described circle Find the radii of a circle inscribed and circumscribed by a regular pentagon whose side measures 3 cm.
• 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?
• Steps Find the height between the two floors if you know that the number of steps between the two floors is 18, the gradient is 30º and the length of the step is 28.6 cm. Report the result in centimeters to the nearest centimeter.
• Right angle In a right triangle ABC with a right angle at the apex C, we know the side length AB = 24 cm and the angle at the vertex B = 71°. Calculate the length of the legs of the triangle.
• A drone A flying drone aimed the area for an architect. He took off perpendicularly from point C to point D. He was at a height of 300 m above the plane of ABC. The drone from point D pointed at a BDC angle of 43°. Calculate the distance between points C and B in
• Hectares of forest 12 workers plant 24 ha of forest in 6 days. In how many days will 15 people and 12 people plant the same area?
• Pentagonal prism The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism.
• 14 percent If 14 percent is 56, what is the base?

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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.