Question

Mark is playing soccer. He is 150 yards from the center goal. When he kicks the ball it goes 145 yards at an angle of 2 degrees off to the right. How far is the ball from the goal?

Answer 1

8 yards

Explanation:

This can be illustrated from drawing it. (Attachment)

Scale- Real : Map

10 yard : 1 cm

150 yard : 15 cm

145 yard : 14.5 cm

Step 1: Draw a 7.5 cm line from origin to Point A

Step 2: Form a 2 degree angle from the origin

Step 3: Draw a 7.25 cm line 2 degree angle from the origin to Point B

Step 4: Measure the distance in cm from Point A to Point B

Step 5: Convert the distance from Point A to Point B in yards.

Therefore, the ball is 8 yards far from the goal.

!!

Answer 2

The ball is 7.176 yards away from the center of the goal.

Explanation:

Given distance between the center goal and Mark is AB = 150 yards

Distance traveled by ball at angle 2 degree off to the right from Mark is

AC = 145 yards

We have to find the distance BC in triangle ABC

Using cosine rule

`BC^(2)=AB^(2)+AC^(2)-2AB* AC* \cos \Theta`

=>
`BC^(2)=[150^(2)+145^(2)-2* 150* 145* \cos (2^(\circ))] yards^(2)`

=>BC^{2}=51.5 yards^{2}

=>
`BC=\sqrt{(51.5 yards^(2))}=7.176yards`

Thus the ball is 7.176 yards away from the center of the goal.