Question

Part A

Answer 1

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 $A$

and the distance of your friend's street be $B$

and let the displacement between your friends house and your house be $C$

The relation in the diagram shows a right angle triangle.

The sides of the right angle triangle are represented as $A,B$ and $C$.

To find $A$, 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,

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

$C$ is the hypotenuse, which is the displacement between your friends house and your house,

Hence, $C = 10.0 km$

$B$ is adjacent, which is the distance of your friends street

then, $B = 6.0 km$

and $A$ is the opposite, which is the distance of your house

From Pythagoras theorem, we can then write that,

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

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

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

$A = 8.0km$

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

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

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

Then,

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

$Sin\theta = 0.8$

Hence, the sine of the angle  θ at the location of the friend's house is 0.8