of a foot) that maximizes this viewing angle.95. Shooting angles and shots on goal: A soccerplayer is on a breakaway and is dribbling justinside the right sideline toward the opposing goal(see figure). As the defense closes in, she has just afew seconds to decide when to shoot. (a) Useinverse functions to find an expression for theshooting angle 0. (b) Use a calculator to helpdetermine the distance d (to tenths of a foot) thatwill maximize the shooting angle for thedimensions shown.Exercise 9524 ft70 ft(goal area)(penalty area)(sideline)

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Asked Oct 16, 2019
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of a foot) that maximizes this viewing angle.
95. Shooting angles and shots on goal: A soccer
player is on a breakaway and is dribbling just
inside the right sideline toward the opposing goal
(see figure). As the defense closes in, she has just a
few seconds to decide when to shoot. (a) Use
inverse functions to find an expression for the
shooting angle 0. (b) Use a calculator to help
determine the distance d (to tenths of a foot) that
will maximize the shooting angle for the
dimensions shown.
Exercise 95
24 ft
70 ft
(goal area)
(penalty area)
(sideline)
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of a foot) that maximizes this viewing angle. 95. Shooting angles and shots on goal: A soccer player is on a breakaway and is dribbling just inside the right sideline toward the opposing goal (see figure). As the defense closes in, she has just a few seconds to decide when to shoot. (a) Use inverse functions to find an expression for the shooting angle 0. (b) Use a calculator to help determine the distance d (to tenths of a foot) that will maximize the shooting angle for the dimensions shown. Exercise 95 24 ft 70 ft (goal area) (penalty area) (sideline)

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Expert Answer

Step 1

The expression for θ is to be written. Since we do not have a direct relation between the sides for angle θ, we will use the angle β.

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70 В From the figure.relation between angles can be written using trigonometric identities as, 70 B tan 70 tan B d 94 0 B tan d 24 70 94 tan (0 B)= d -1 =__ 24

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Step 2

It can be seen that

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0=(0+B)-B Substitute for (0+B) andBfrom stepl 94 -tan d 70 e=tan d

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Step 3

Using the relation for tan-1x-tan-1y exp...

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-x-y 1+xy tan(x)tany) = tan 94 0= tan d 70 -1 tan 94 70 d d 94 70 1+ d d -1 = tan ө 24 d 6580 e=tan 24d ө- = tan 6580+d 24d tan e 6580+d2

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