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Right so for this problem ladies and gentlemen oops. What we have is we have have the problem here with number 23. So number 23.
Say the height of an basketball backboard. So lets go and draw a backward. So the first thing.
Were obviously going to do right. Its just draw a picture did you go. And describe it so we have a nice.
Little. Backboard and says hi to outdoor backboard is 12 and 1 2. Feet.
Now. I really do not like using feet.
So what im gonna do is im gonna want to put this into inches. All right so go and convert them from feet to inches. All right well you can say how many inches are in one foot 12.
So i have 12 of them so do 12 times. 12. Which is going to be 144 half of a foot would be 6.
So actually this is going to be a hundred and fifty inches. Its gonna be very helpful when you compute all right compute the length or anything else youre gonna be using okay. So then we could say then it says and a backboard casts a shadow 17 and 1 3.
Feet long. So you got a nice sun right here. And its gonna cast a shadow.
Now the length of the shadow. Not the length of the shadow ray.
But the length of the shadow is 17 and 1 3 feet. Which again if i want to convert it to inches. Ill do 12 times 17 is going to give me 204 and then the third of a foot is going to be an extra 4 inches.
So thats going to be two hundred and eight inches okay so therefore ladies and gentlemen. I have 150 inches and 208 inches. Remember ladies and gentlemen when were creating our picture.
The main important thing that we have to make sure we have is right triangles all right we have to be able to use our right triangles. I solve for this so i can see my backboard thats going to create a 90 degree angle right there so it says use trigonometric functions to write the equation. Involving the unknown angle.
All right of the sun find the angle of elevation of the sun. So what we do is we want to find angle of elevation. So remember angle of elevation.
We have to have a horizontal line and angle of elevation is going to be the angle above your horizontal. Which in this case will be theta.
So therefore i have theta and i have my opposite side and my adjacent side. So therefore. I can say tangent of theta is equal to 150 over 200 and 8 inches right.
But ladies and gentlemen. What are we trying to figure out theyre trying to find this angle of elevation so how do we rewrite this to find theta anybody have an idea you write data beta equals inverse tangent of 150 over 208. All right youre not gonna want to use your fractions in here.
See how this is kind of when you do your ratio right youre not gonna want to use 12 and a half with your fractions. Youre gonna want to convert them over so therefore to complete this problem. Ill just do 150.
Divided by 200 8. And then i take. Inverse tan and then inverse tan.
So i can answer not giving me. What i have oh.
I did wrong one 150 divided by two zero eight. And you got to make sure your degree your calculator is in degree mode and you get thirty one point. Nine nine six so therefore im going to say theta is approximately 32 degrees.
Okay yes. What you get for 150 divided by 208 did you have 150 divided by 208. Okay.
172. 1 1. Right and then you do inverse tangent of second answer so inverse tangent yeah.
Im getting 35. I dont know howd it happen there i might have typed into the wrong number again so yes. Youre right theta equals.
Lets do thirty five point eight zero and lets approximate that with this quickly okay. What do you mean what well were not what is theta representing website increase if you want to use your feet or convert them to centimeter i mean thats whatever doesnt matter. Its not gonna change the answer just you need to remember were finding theta.
Which is going to be in degrees okay got it michael .
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