Basic operations and concepts - math word problems - page 329 of 331

Number of problems found: 6620

Railway line
The straight railway line has a gradient of 16 per mille. What is the size of the pitch angle?
Triangle in circle
The vertices of the triangle ABC lie on a circle with a radius 3, which is divided into three parts in the ratio 4:4:4. Calculate the circumference of the triangle ABC.
Goat
The meadow is a circle with a radius r = 20 m. How long must a rope tie a goat to the pin on the meadow's perimeter to allow the goat to eat half of the meadow?
Observer
The observer sees a straight fence 100 m long in 30° view angle. From one end of the fence is 119 m. How far is it from the other end of the fence?
Straight road
The straight road has a rise of 19%. How big is the pitch angle?
Angle of climb
At what angle does the road rise if the climb is 10%?
Road drop
A 12 percent drop is marked on a straight stretch of road. What angle aligns the direction of the road with the horizontal plane?
Road
A gradient of 1:19 represents the average climb of the road. By what angle does the road moderate climb?
Ratio iso triangle
The ratio of the sides of an isosceles triangle is 7:6:7. Find the base angle to the nearest answer correct to 3 significant figures.
Observation angle
At what angle of view does an object 70 m long appear to the observer, 50 m away from one end and 80 m from the other end?
CuSO4 mixture
How many grams of solid CuSO₄ must be added to 450 g of a 15% CuSO₄ solution to produce a 25% solution?
Climb of the road
At what angle does the road rise if the climb is 8%? They rounded up for tens of minutes.
Triangle angles
In the triangle ABC, a: b = 3:2 and α: β = 2:1. Calculate the ratio a: c.
Maximum area of rhombus
At what interior angles does a rhombus have the maximum area?
Sides ratio and angles
In triangle ABC, you know the ratio of side lengths a:b:c=3:4:6. Calculate the angle sizes of triangle ABC.
Equilateral triangle
A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.
Largest angle of the triangle
Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a
Rhombus
Internal angles of a rhombus are in the ratio 2:5. How many times is the shorter diagonal longer than the side of the rhombus?
Sine theorem 2
From the sine theorem, find the ratio of the sides of a triangle whose angles are 30°, 60°, and 90°.
Trigonometric formula
Determine the value of the function tg x (tangent) when cotan x = -0.8 (cotg or cotangent); x holds in the second quadrant)

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