Goniometry and trigonometry - math word problems - page 11 of 32
Number of problems found: 634
- Loonie
Loonie has three wooden sticks measuring 17 inches, 21 inches, and 25 inches. He lays them down to form a triangle. Find the measure of the angle enclosed by 17 inches and 21 inches. (Express answers to the nearest hundredths) (using the law of cosines) - Telegraph poles
The bases of two adjacent telegraph poles have a height difference of 10.5 m. How long do the wires connect the two poles if the slope is 39° 30’? - Landing strip
How long is the runway at an airport if, at an altitude of 1.2 km, the beginning of the runway is visible at a depression angle of 58° and the end at a depression angle of 27°? - The tower
From a window 8 m above the horizontal plane, the top of a tower can be seen at an elevation angle of 53°20′, and its base at a depression angle of 14°15′. How high is the tower? - Lodge view angle
The observer lies on the ground at a distance of 20 m from a hunting lodge 5 m high. A) At what angle of view does the posed see? B) How much does the angle of view change if it approaches the sitting by 5 m? - Observation tower
The observation tower has a height of 105 m above sea level. The ship is aimed at a depth angle of 1° 49' from the tower. How far is the ship from the base of the tower? - The bases
The bases of the isosceles trapezoid ABCD have 10 cm and 6 cm lengths. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and area of the ABCD trapezoid. - Power line pole
From point A, the power pole is visible at an angle of 18 degrees. From place B, which we reach if we go from place A 30 m towards the pillar at an angle of 10 degrees. Find the height of the power pole. - Raindrops
The train runs at a speed of 14 m/s, and raindrops draw lines on the windows, forming an angle of 60 degrees with the horizontal. What speed do drops fall? - Triangle ABC v2
The area of the triangle is 12 cm². Angle ACB = 30º , AC = (x + 2) cm, BC = x cm. Calculate the value of x. - Clouds
From two points, A and B, on the horizontal plane, a forehead cloud was observed above the two points under elevation angles 73°20' and 64°40'. Points A and B are separated by 2830 m. How high is the cloud? - Pentadecagon
Calculate the area of a regular 15-side polygon inscribed in a circle with a radius r = 4. Express the result to two decimal places. - Shooter
The shooter fired at a target from a distance 49 m. The individual concentric circle of targets has radius increments of 1 cm (25 points) by 1 point. The shot was shifted by 16' (angle degree minutes). How many points should he win his shot? - Isosceles trapezoid
Find the height in an isosceles trapezoid if the area is 520 cm² and the base a = 25 cm and c = 14 cm. Calculate the interior angles of the trapezoid. - A flagpole
A flagpole is leaning at an angle of 107° with the ground. A string fastened to the top of the flagpole is holding up the pole. The string makes an angle of 38° with the ground, and the flagpole is 8 m long. What is the length of the string? - Cosine
Cosine and sine theorem: Calculate all unknown values (side lengths or angles) from triangle ABC. c = 2.9 cm; β = 28°; γ = 14° α =? °; a =? cm; b =? cm - Diagonal BD
Find the length of the diagonal BD in a rectangular trapezoid ABCD with a right angle at vertex A when/AD / = 8,1 cm and the angle DBA is 42° - Diamond area calculation
The ABCD diamond has a circumference of 72 cm. The longer diagonal of the animal with the line segment AB angle is 30 °. Calculate the area of the ABCD diamond. - 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. - Triangle α and side
Side a in the right triangle has size a = 120 mm, angle α = 60°. How big is the hypotenuse c?
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