Question

A car is driven 250 km west and then 98 km southwest (45∘) what is the displacement of the car from the point of origin (magnitude)

Answer 1

To answer this item, we first determine the x and y components of each of the vectors. 

First vector: 250 km west
   x-component = -250 km
   y - component = 0 km

Second vector: 98 km southwest
    x-component = (-98)(cos 45°)
          x-component = -69.286 km
    y-component = (-98)(sin 45°)
          y-component = -69.286 km

Adding up the components:
  x-component = -250 km + (-69.289 km) = -319.286 km
  y-component = -69.286 km

Taking the resultant of the vectors,
         resultant = sqrt ((-319.286 km)² + (-69.286 km)²)
                        = sqrt (101943.55 km² + 4800.55 km²)
                        = 326.72 km

Answer: 326.72 km

Answer 2

The displacement of the car from the point of origin (magnitude) = 326.729 km

Further explanation

Triangles are flat fields bounded by 3 intersecting sides and 3 angles

This side can be the same length or different.

If at an angle there is an angle of 90 degrees, this triangle is said to be a right angle

There is a hypotenuse in this triangle which is the sum of the two sides

c² = a² + b²

where c = hypotenuse

This formula is known as the Pythagorean theorem which states that:

the hypotenuse or the longest side in a right triangle equal to the sum of the squares of the other sides.

While the angle formulas used are

sin a = front side / hypotenuse

cos a = side / hypotenuse

tan a = front / side

(The attached image )

We see the triangle ABC

to find the value of x we ​​use the phytagorean formula

x² + x² = 98²

2x² = 98²

$x^2=\frac{98^2}{2}$

$x=\frac{98\sqrt{2} }{2}$

We add the x value on the x-axis to find the DE side

De = x + 250

$DE=\frac{98\sqrt{2} }{2}+250$

DE = 319.2965

So the DC side is a slash from the ADC triangle

DC² = DE² + EC²

$DC^2=319.29652+\frac{98\sqrt{2} }{2}$

DC² = 106752.255

DC = 326,729

Learn more

the Sin rule

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trigonometric ratio

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the triangle angle

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Prove the converse of the Pythagorean Theorem

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Use Pythagoras' theorem

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Keywords: Pythagoras' theorem, the trigonometric, hypotenuse