# Absolute value + Pythagorean theorem - examples

1. Triangle
Triangle KLM is given by plane coordinates of vertices: K[-12, -11] L[-15, -18] M[-13, -12]. Calculate its area and itsinterior angles.
The rectangular crossroads comes passenger car and an ambulance, the ambulance left. Passenger car is at 43 km/h and ambulance 52 km/h. Calculate such a relative speed of the ambulance moves to the car.
An airplane leaves an airport and flies due west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?
4. Vector
Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
5. Goniometric form
Determine goniometric form of a complex number ?.
6. Cube - wall
V kocke ABCDEFGH je ?. Aký je povrch kocky?
7. Unit vector 2D
Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10].
8. Vectors
Vector a has coordinates (8; 10) and vector b has coordinates (0; 17). If the vector c = b - a, what is the magnitude of the vector c?
9. 3d vector component
The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?
10. Right triangle - leg
Calculate to the nearest tenth cm length of leg in right-angled triangle with hypotenuse length 9 cm and 7 cm long leg.
11. Moivre 2
Find the cube roots of 125(cos 288° + i sin 288°).
12. Find the 5
Find the equation with center at (1,20) which touches the line 8x+5y-19=0
13. Three points
Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k?

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Pythagorean theorem is the base for the right triangle calculator.