Mathematics
25.05.2023 08:20
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An airplane started at point X, traveled 320 miles to point Y, adjusted its route,

An airplane started at point X, traveled 320 miles to point Y, adjusted its route, and traveled another 400 miles to point Z. If the airplane is currently 599 miles from its starting position at point X, by how many degrees did it adjust its route at point Y?
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lukas27
lukas27
5,0(23 marks)

67.88°

Step-by-step explanation:

If three sides of a triangle are known and you want to determine one angle, this can be done using cosine rule.

Given sides x, y, and z and the angle Y is opposite to side y, the cosine formula is given as:

y² = x² + z² - 2xzcosY

For this problem, x = 400 miles, y = 599 miles, z = 320 miles.

Using the cosine formula:

y^2=x^2+z^2-2xzcos(Y)\\Substituting:\\599^2=400^2+320^2-2(400)(320)cos(Y)\\2(400)(320)cos(Y)=400^2+320^2-599^2\\256000cos(Y)=-96401\\cos(Y)=-0.3766\\Y=cos^{-1}(-0.3766)\\Y=112.12^0

Degree to adjust its route at point Y = 180° - 112.12° = 67.88°

It needs to adjust by 67.88° at point Y

isabellajmoody
isabellajmoody
5,0(98 marks)
The answer to the sum 3568 × 39610 =141 328 480, so neither of them correct

both tried to use partition method to multiply the two numbers but neither of them has  partitioned the values correctly

3568 = 3000+500+60+8
39610 = 3+9000+600+10

then we multiply in turn each value from 3568 to the values of 39610
3000  × 3
3000  × 9000
3000  × 600
3000  ×10 

and so on

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