Answer:
Part A
You have to ride 8.0 km before turning north to get to your friend’s house.
Part B
The sine of the angle θ at the location of the friend's house is 0.8
Explanation:
The remaining part of the question which is an image is attached below
Explanation:
Part A
To determine how far you will ride ride before turning north,
From the diagram, that is the distance of your street.
Let the distance of your street be [tex]A[/tex]
and the distance of your friend's street be [tex]B[/tex]
and let the displacement between your friends house and your house be [tex]C[/tex]
The relation in the diagram shows a right angle triangle.
The sides of the right angle triangle are represented as [tex]A,B[/tex] and [tex]C[/tex].
To find [tex]A[/tex], which is the distance of your street,
From Pythagorean theorem, 'The square of hypotenuse is the sum of squares of the other two sides'
That is,
[tex]/Hypoyenuse/^{2} = /Adjacent/^{2} + /Opposite/^{2}[/tex]
[tex]C[/tex] is the hypotenuse, which is the displacement between your friends house and your house,
Hence, [tex]C = 10.0 km[/tex]
[tex]B[/tex] is adjacent, which is the distance of your friends street
then, [tex]B = 6.0 km[/tex]
and [tex]A[/tex] is the opposite, which is the distance of your house
From Pythagoras theorem, we can then write that,
[tex]C^{2} = B^{2} + A^{2}[/tex]
Then, [tex]10.0^{2} = 6.0^{2} + A^{2}[/tex]
[tex]A^{2} = 100.0 - 36.0\\A^{2} = 64.0\\A = \sqrt{64.0}[/tex]
[tex]A = 8.0km[/tex]
Hence, you have to ride 8.0 km before turning north to get to your friend’s house.
Part B
To find the sine of the angle θ at the location of the friend's house,
In the diagram, the sine of the angle θ is given by
[tex]Sin\theta = \frac{Opposite}{Hypotenuse}[/tex]
Hence, [tex]Sin\theta = \frac{A}{C}[/tex]
Then,
[tex]Sin\theta = \frac{8.0}{10}[/tex]
[tex]Sin\theta = 0.8[/tex]
Hence, the sine of the angle θ at the location of the friend's house is 0.8
A. The amount of distance you have to ride before turning North to get to your friend’s house is 8 kilometers.
B. The sine of the angle (θ) at the location of your friend's house is 0.8.
Given the following data:
A. To determine the amount of distance you have to ride before turning North to get to your friend’s house, we would apply Pythagorean's theorem:
Mathematically, Pythagorean's theorem is given by the formula:
[tex]c^2 = a^2 + b^2\\\\10^2 =6^2+b^2\\\\100=36+b^2\\\\b^2 =100-36\\\\b^2 =64\\\\b=\sqrt{64}[/tex]
b = 8 kilometers
B. To find the sine of the angle (θ) at the location of the friend's house:
Mathematically, the sine of an angle is given by the formula:
[tex]Sin\theta = \frac{opposite}{hypotenuse}[/tex]
Substituting the given parameters into the formula, we have;
[tex]Sin\theta = \frac{8}{10} \\\\Sin\theta = 0.8[/tex]
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