Square root - practice problems - page 6 of 73

Number of problems found: 1450

Cplx sixth power
Let z = 2 - sqrt(3i). Find z⁶ and express your answer in rectangular form. if z = 2 - 2sqrt(3 i) then r = |z| = sqrt(2 ^ 2 + (- 2sqrt(3)) ^ 2) = sqrt(16) = 4 and theta = tan -2√3/2=-π/3
A triangle 7
A triangle lot has the dimensions a=15 m, b=10 m, and c=20 m. What is the measure of the angle between the sides of b and c?
Deep pool - bottom
A pool is 25 m long and 12 m wide. In one half of the pool, the depth is constant at 1.8 m; in the other half, the bottom slopes gradually up to a depth of 1.2 m. What is the total area of the pool bottom?
Triangle ABP
An isosceles trapezoid ABCD is given. The length of side AB is 10 cm, the length of CD is 7 cm, and the height drawn to side AB is 4 cm. Point P is the foot of the altitude from A to side AD. Calculate the area of triangle ABP.
Hexagon, hexa S, V
What is the surface area and volume of a regular hexagonal prism with a base edge of 12 cm and a height equal to the diameter of the circle circumscribed about the base?
Tunnel - quadrilateral
How long will tunnel AB be, given distances AD = 35 m, DC = 120 m, CB = 85 m, angle ADC = 105°, and angle BCD = 71°, where ABCD is a quadrilateral?
216 surface area and volume
Calculate the surface area and volume of a regular tetrahedral pyramid with base edge a = 6 cm and height of 12 cm.
4B - truncated pyramid
Calculate the volume of a regular truncated quadrilateral pyramid if the base edges are 10 cm and 4 cm and the slant height of the lateral face is 5 cm.
Legs and ratio
The legs of a right triangle are in the ratio a:b = 6:8. The hypotenuse has a length of 61 cm. Calculate the perimeter and area of this triangle.
RRL Basics
What is the length of the smaller base and the height of an isosceles trapezoid if a = 9 dm, the leg is 6 dm, and angle ACB = 90°?
In a regular 5
In a regular triangular prism ABCV, the angle between the lateral face and the base plane is α = 45°. Determine the angle between the lateral edge and the base plane.
Construct 22
Construct a rhombus ABCD if the diagonals are f = 7 cm and e = 5 cm.
Base RR odd
The base of a prism is an isosceles trapezoid ABCD with bases AB = 12 cm and CD = 9 cm. The angle at vertex B is 48°10′. Determine the volume and surface area of the prism if its height is 35 cm.
RR trapezoid 12
In an isosceles trapezoid ABCD, calculate the missing side lengths given a = 46 cm, b = 85 cm, and height = 84 cm.
Area 51
The area of a triangle is 54.39, angle alpha is 32°, and angle gamma is 144°.
Calculate
A cone has a base diameter of 16 cm and a slant height of 10 cm. Calculate its surface area and volume.
Quadrilateral - irregular
Find the length of side d = |AD| in quadrilateral ABCD: a = 35 m, b = 120 m, c = 85 m, angle ABC = 105°, angle BCD = 72°.
Rhombus 48
A large rhombus is composed of four identical smaller rhombuses, each with an area of 42 m² and an angle alpha of 60°. What is the perimeter of the large rhombus?
Observation tower
An observation tower is covered with a roof in the shape of a regular quadrilateral pyramid with a base edge of 8 m and a height of 6 m. 60% of the roofing needs to be replaced. How many m² of new roofing material need to be bought?
A chest made
A chest in the shape of a cuboid made of sheet iron has dimensions of 2.4 m × 0.8 m × 0.5 m. What will be the volume of a cube-shaped chest with the same surface area?

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