approximately what is the angle between two position vectors if their terminal points are (1,5) and (6,3)
1 answer:
Answer:
The angle between them = 52.1°
Step-by-step explanation:
∵ The position vector of the first point is
∵ The position vector of the second point is
∵ The magnitude of the first = √(1²+5²) = √26
∵ The magnitude of the second = √(6²+3²) = √45
∵ The scalar product of them = (1 × 6) + (5 × 3) = 6 + 15 = 21
∵ cosФ = scalar product/(magnitude 1st × magnitude 2nd)
∴ cosФ = 21/(√26 × √45) = 0.61394
∴ Ф = 52.1°
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The measure of hypotenuse using the ruler is 25.5 cm and using the formula is 23.43 cm, they are not same, and formula can be used to in the real life problems as well.
<h3>What is a right-angle triangle?</h3>It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
The question is incomplete:
The complete question is:
Present a picture of an object (TV, Ipad Screen, Book Cover) that contains a right angle (it could be something in nature or that is man-made). Use a ruler or measuring tape to measure the two sides that make the right angle and measure the distance from the end of one side to the end of the other side (hypotenuse). Draw a diagram of the object including the measurements. Use your leg measurements on your diagram to calculate a theoretical hypotenuse. (Show all steps).
- Does the hypotenuse that measured with a ruler/measuring tape equal the hypotenuse you calculated?
- Why do you think they are or are not exactly the same?
- What did you learn from developing this presentation?
We are assuming the length of one side x:
x = 18 cm
Length of other side y:
y = 15 cm
And length of the hypotenuse z:
z = 23.5 cm
From the Pythagoras theorem:
z² = x² + y²
z² = 18² + 15²
z² = 549
z = √54 = 23.43 cm
The measure of hypotenuse is:
Using ruler: x = 25.5 cm
Using formula: x = 23.43 cm
They are not equal due to the reading in the ruler.
The formula can be used to in the real life problems as well.
Thus, the measure of hypotenuse using the ruler is 25.5 cm and using the formula is 23.43 cm, they are not same, and formula can be used to in the real life problems as well.
Learn more about the right angle triangle here:
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