Physical quantities - math word problems - page 174 of 177

Number of problems found: 3535

Sun and shadow
The pole is stuck vertically into the ground. The protruding length is 1 m. What is the length of the shadow cast when the sun is just 50° above the horizon?
What is 19
What is the length of the hypotenuse c of right triangle ABC if the angle α at vertex A is 30° and leg a = 3 cm?
Big tree
You are standing 20 feet away from a tree, and you measure the elevation angle to be 38°. How tall is the tree?
Triangle angle sides
In the right triangle ABC, calculate the magnitude of the interior angles if / AB / = 13 cm; / BC / = 12 cm and / AC / = 5 cm.
Perimeter of a circle segment
A circle with a diameter of 30 cm is cut by a chord t = 16 cm. Calculate the perimeter and area of the smaller segment.
Cone semicircle proof
If the shell of a cone is a semicircle, then the diameter of the cone's base is equal to its side's length. Prove it.
Triangle tangent area
The tangent of the angle formed by the adjacent sides of the triangle ABC (side a=29 m, b = 40 m) equals 1.05. Calculate the area of that triangle.
Big tower
From a tower 15 meters high and 30 meters away from the river, the width of the river appeared at an angle of 15°. How wide is the river in this place?
Circumscribed decagon
In a regular decagon, the diameter of the circumscribed circle measures 10 cm. Determine the radius of the circle inscribed in this decagon.
Factory chimney
How tall is a factory chimney if its top is seen from a distance of 60 metres at an elevation angle of 60°?
Cis notation
Evaluate the multiplication of two complex numbers in cis notation: (6 cis 120°)(4 cis 30°) Write the result in cis and Re-Im notation.
The ladder
The ladder makes an angle of 2°30' with the wall and reaches a height of 2.3 m. How far is the ladder from the wall?
SAS calculation
Given the triangle ABC, if side b is 31 ft., side c is 22 ft., and angle α is 47°, find side a. Please round to one decimal.
North Pole
What is the shortest distance across the globe's surface on a scale of 1:1,000,000 from the equator to the North Pole?
Right Triangle Angle
In a right triangle ABC, hypotenuse c = 8 cm and leg b = 4 cm. What is the size of angle α?
Base and legs
A right triangle has a base/legs/length of 12 cm, and the angle with the hypotenuse is 13 degrees. What is the length of the second hypotenuse?
The staircase
The staircase has a total height of 3.6 m and forms an angle of 26° with the horizontal. Calculate the length of the whole staircase.
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?
Oscillator deflection
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 = 0.02 s, b) t2 = 0.04 s, when it was zero at time t = 0 s?
A rectangle 5
A rectangle has sides of 10 cm and 14 cm. Calculate the angle between a diagonal and a long side.

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