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
[tex]x^2=\frac{98^2}{2}[/tex]
[tex]x=\frac{98\sqrt{2} }{2}[/tex]
We add the x value on the x-axis to find the DE side
De = x + 250
[tex]DE=\frac{98\sqrt{2} }{2}+250[/tex]
DE = 319.2965
So the DC side is a slash from the ADC triangle
DC² = DE² + EC²
[tex]DC^2=319.29652+\frac{98\sqrt{2} }{2}[/tex]
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
