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

Answer:

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

Step-by-step 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

$BC^{2}=AB^{2}+AC^{2}-2AB\times AC\times \cos \Theta$

=>$BC^{2}=[150^{2}+145^{2}-2\times 150\times 145\times \cos (2^{\circ})] yards^{2}$

=>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.

Answer 2

Answer:

8 yards

Step-by-step 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.

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