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2 months ago

Part A

Physics

1 answer:

kicyunya [3.2K]2 months ago

4 0

Answer:

Part A

You'll travel 8.0 km before you can turn to the north to reach your friend's residence.

Part B

At your friend's house, the sine of the angle θ measures 0.8.

Explanation:

The remaining part of the question including an image is displayed below.

Explanation:

Part A

To calculate how far you'll go before making the northward turn,

the diagram illustrates the length of your street.

Let the length of your street correspond to $A$

and your friend's street length be denoted as $B$

with the distance separating your house from your friend's indicated as $C$ .

The diagram illustrates a right triangle.

The sides of this triangle can be represented by $A,B$ and $C$ .

To identify $A$ , the extent of your street,

we can apply the Pythagorean theorem: 'The area of the hypotenuse equals the total of the squares of the other two sides.'

This leads to:

$/Hypoyenuse/^{2} = /Adjacent/^{2} + /Opposite/^{2}$

Here, $C$ represents the hypotenuse, which is the distance between your house and your friend’s house,

thus, $C = 10.0 km$

$B$ indicates the adjacent side, which is your friend's street distance.

Furthermore, $B = 6.0 km$

and $A$ represents the opposite side, corresponding to your house's distance.

$C^{2} = B^{2} + A^{2}$

Then, $10.0^{2} = 6.0^{2} + A^{2}$

$A^{2} = 100.0 - 36.0\\A^{2} = 64.0\\A = \sqrt{64.0}$

$A = 8.0km$

Therefore, you need to ride 8.0 km before turning north to reach your friend's house.

Part B

In order to calculate the sine of the angle θ at your friend’s location,

the diagram indicates that the sine of angle θ can be expressed as

$Sin\theta = \frac{Opposite}{Hypotenuse}$

Consequently, $Sin\theta = \frac{A}{C}$

Then,

$Sin\theta = \frac{8.0}{10}$

$Sin\theta = 0.8$

Thus, the sine value at your friend's house is 0.8

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