Physical quantity - math word problems - page 329 of 342
Number of problems found: 6824
- 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. - Inscribed and described circle
Find the radii of a circle inscribed and circumscribed by a regular pentagon whose side measures 3 cm. - Isosceles 4741
The arm is five times longer than its base in an isosceles triangle. Calculate its interior angles. - Rhomboid
The rhomboid sides' dimensions are a= |AB|=5cm, b = |BC|=6 cm, and the angle's size at vertex A is 60°. What is the length of the diagonal AC? - De Moivre's formula
There are two distinct complex numbers, such that z³ is equal to 1 and z is not equal to 1. Calculate the sum of these two numbers. - Trigonometric functions
In the right triangle is: tg α= frac(4) 2 Find the value of s and k: sin α= (s)/(√ 20) cos α= (k)/(√ 20) - Calculate 82696
In the triangle ABC, b=5 cm, c=6 cm, /BAC/ = 80° are given. Calculate the sizes of the other sides and angles, and further determine the sizes of the tangent tc and the area of the triangle.
- Alpha angle
Right triangle. Given: side c = 15.8 and angle alpha = 73°10'. Calculate side a, b, angle beta, and an area. - Determine 8133
Determine the distance between two places, M, and N, between which there is an obstacle so that place N is not visible from place M. The angles MAN = 130°, NBM = 109°, and the distances |AM| = 54, |BM| = 60, while the points A, B, and M lie on one straigh - Construct 13581
The vertices of the triangle ABC lie on the circle k. The circle k is divided into three parts in a ratio of 1:2:3. Construct this triangle. - A chord
In a circle radius of 6 cm, a chord is drawn 3 cm from the center. Calculate the angle subtended by the chord at the center of the circle. Hence find the length of the minor arc cut off by the chord. - A dodecagon
Find the surface area of a regular 12-sided polygon if its side is a = 12 cm. - Distribute 32451
The king cannot decide how to distribute 4 cubes of pure gold, which have edges of length 3cm, 4cm, 5cm, and 6cm, to two sons as fairly as possible. Design a solution so that the cubes do not have to be cut. - Elevation angle
An airliner currently flying over a location 2,400 m away from the observer's location is seen at an elevation angle of 26° 20'. At what height does the plane fly? - Observation 76644
From the smaller observation tower, we see the top of the larger tower at an elevation angle of 23°, and the difference in their heights is 12 m. How far apart are the observation towers?
- Greatest angle
Calculate the greatest triangle angle with sides 124, 323, 302. - Horizontal 66434
The lower station of the cable car in Smokovec is at an altitude of 1025m, and the upper station at Hrebienk is at an altitude of 1272m. Calculate the climb of the cable car if the horizontal distance between the slopes is 1921m. - Hypotenuse and center
Point S is the center of the hypotenuse AB of the right triangle ABC. Calculate the area of triangle ABC if the line on the hypotenuse is 0.2 dm long and if angle ∢ACS is 30°. - One side
One side is 36 long with a 15° incline. What is the height at the end of that side? - High wall
I have a wall 2m high. I need a 15-degree angle (upward) to the second wall 4 meters away. How high must the second wall be?
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