Question

a soccerball is placed 10 feet away from the goal, which is 8 feet high. you kick the ball and it hits the crossbar along the top of the goal. what is the angle of evaluation of the kick?

Answer 1

First draw the image. The goal post is 8 feet high and the soccer ball is 10 feet away. When you kick the ball, it hits the top of the goal. And we're looking for the angle

Does the image look correct to you?

Answer 2

ok

Answer 3

So we have an angle

Which side values do we have?

We have everything but the hypotenuse so we have the opposite side and the adjacent side

So do we use sin, cos or tan?

Answer 4

tan

Answer 5

Exactly!! Good job :)

so let's call this angle 'x' (where I drew the ? in the image)

tan x = opposite/adjacent

What side is opposite the angle x?
And what side is adjacent to the angle?

Answer 6

the opposite is 8?

Answer 7

Exactly! And the adjacent side would be 10

So can you write it out?

tan x = ??

Answer 8

8/10?

Answer 9

Yes and what is that as a decimal?

Answer 10

0.8

Answer 11

So we have

tan x = 0.8

Do you agree?

Answer 12

yes

Answer 13

Now, I don't think you've learned this but the way to solve for x requires using arctan or \(\tan^{-1}\)

You might see it written either way but it's the same thing

But this is what's happening essentially

So you know how if we take the tan of an angle, we'll get a value?

But how do we calculate what angle it takes to get that value?

So we have to use arctan or \(\tan^{-1}\)

Answer 14

ok?

Answer 15

So let me just some letters for numbers 'a' and 'b' to show you how it works

if \(\tan (a) = b\)

then that means
\(\tan^{-1} (b) = a\)

or another way to write it would be
\(\arctan (b) = a\)

Answer 16

So at this point all you have to do is use a calculator, but you don't use tan

you have to use arctan to find the angle

and remember to be in degrees, not radians!

So we had

tan x = 0.8

that means

arctan(0.8) = x

Does that make sense?

Answer 17

https://www.google.com/search?q=arctan%280.8%29+in+degrees

Answer 18

arctan and \(\tan^{-1}\) are basically the inverse tan

so you do the inverse tan so that way you can find the angle

Answer 19

so 38.6

Answer 20

Yep! Although I would probably round it to 38.7

Answer 21

ok thanks again AZ your really helping me out i just one more question to post

Answer 22

You're welcome!