Pythagorean theorem + unit conversion - practice problems - page 4 of 7
Number of problems found: 134
- ABS, ARG, CONJ, RECIPROCAL
Let z=-√2-√2i where i2 = -1. Find |z|, arg(z), z* (where * indicates the complex conjugate), and (1/z). Where appropriate, write your answers in the form a + i b, where both a and b are real numbers. Indicate the positions of z, z*, and (1/z) on an Argand - Sailboat
The 20 m long sailboat has an 8 m high mast in the middle of the deck. The top of the mast is fixed to the bow and stern with a steel cable. Determine how much cable is needed to secure the mast and what angle the cable will make with the ship's deck. - Isosceles trapezoid
The old father decided to change the top plate of an isosceles-like trapezoid with the basic dimensions of 120 cm and 60 cm, and the shoulder is 50 centimeters long. How much does it pay for a new plate and a square meter worth 17 euros? - Cross road
From the junction of two streets perpendicular to each other, two cyclists (each on another street) walked out. One ran 18 km/h and the second 24 km/h. How are they away from a) 6 minutes, b) 15 minutes?
- Widescreen monitor
Computer businesses were hit by a wave of widescreen monitors and televisions. Calculate the area of the LCD monitor with a diagonal size 20 inches at a ratio of 4:3 and then a 16:9 aspect ratio. Is buying widescreen monitors with the same diagonal more - Trapezoid MO
The rectangular trapezoid ABCD with the right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid. - Airport's 80482
The plane flew from airport m on a course of 132° to airport n, then from n to p on a course of 235°. The distance between the airport's mn is 380 km, np 284 km. What will be the return course to m, and what is the distance between the airport's pm? - Solve 13
Solve the missing dimensions for the following triangle: Triangle ABC: AngleA=43 degrees, b=7.0cm, c=6.0cm Question 1. Angle B with units written as degrees Question 2. Angle C with units written as degrees Question 3. a, rounded to the nearest tenth of a - Archaeologists 81478
Archaeologists need to find out the size of the vessel if the sherd found was in the shape of a circular section with a length of 12 cm and a height of 3 cm. What is the area of this section?
- Inaccessible 82710
Determine the distance between two inaccessible places K, L, if the angles KAL=62°10", LAB=41°23", KBL=66°34", and LBA were measured from points A, B, which are 870 m apart = 34°52". Thank you. - Parallelogram 82695
Given is the parallelogram KLMN, in which we know the side sizes/KL/ = a = 84.5 cm, /KN/ = 47.8 cm, and the angle size at the vertex K 56°40'. Calculate the size of the diagonals. - Movement
From the crossing of two perpendicular roads started two cyclists (each on a different road). One runs at an average speed of 28 km/h, and the second 24 km/h. Determine the distance between them after 45 minutes of cycling. - Two aircraft
Two planes fly to the airport. At some point, the first airplane is away from the airport by 98 km and the second 138 km. The first aircraft flies at an average speed of 420 km/h, and the second average speed is 360 km/h, while the tracks of both planes a - Minutes 38331
Two planes took off from Prague at one point. The first is flying north at a speed of 420 km/h, and the second is flying east at a speed of 560 km/h. How far apart will they be as the crow flies in 25 minutes of flight?
- A hiker
A hiker plans to hike up one side of a mountain and down the other side of points a mountain, each side of the mountain formed by a straight line. The angle of elevation at the starting point is 42.4 degrees, and the angle of elevation at the end is 48.3 - Observatory 71934
The aircraft flying towards the observatory was aimed at a distance of 5300 m at an elevation angle of 28º and after 9 seconds at a distance of 2400 m at an elevation angle of 50º. Calculate the distance the plane has flown in this time interval, its spee - Inaccessible 69794
Determine the distance between two inaccessible places P, Q, if the distance between two observation points A, B is 2000m and if you know the size of the angles QAB = 52°40''; PBA = 42°01''; PAB = 86°40'' and QBA = 81°15''. The considered locations A, B, - Gimli Glider
Aircraft Boeing 767 lose both engines at 42000 feet. The plane captain maintains optimum gliding conditions. Every minute, lose 1910 feet and maintain constant speed 211 knots. Calculate how long it takes for a plane to hit the ground from engine failure. - Triangle
Plane coordinates of vertices: K[19, -4] L[9, 13] M[-20, 8] give Triangle KLM. Calculate its area and its interior angles.
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