:(:( trig problems that are killing me

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sbeaubrun

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I HAVE TWO PROBLEMS THAT HAVE RACKED MY BRAIN, I MISSED ONE DAY OF SCHOOL TRYING TO GET A WISDOM TOOTH TAKEN OUT AND I HAVE BEEN LOST EVER SINCE. I HAVE AN EXAM COMING UP AND HAVE BEEN TRYING TO GET HELP BECAUSE I KNOW THESE TWO QUESTIONS IF NOT SIMILAR ONES WILL BE ON THE TEST. A FRIEND GAVE ME THE ANSWERS BUT I NEED TO UNDERSTANDDDDDD HOW TO PROPERLY SOLVE IT AND THAN MAKE SURE THAT THE ANSWER WAS EVEN CORRECT. ANY HELP YOU CAN GIVE WOULD BE AWESOME:

A wire attached to the top of a tower makes an angle of 65 degrees with the ground. At a point on the ground 100 feet away from the end of the wire, the angle of elevation to the top will be 32 degrees. how would one find the height of the tower, to the nearest foot.


sarah and amerie were standing one mile apart on eastern parkway. they saw a jet blue aircraft between them directly above the road. The angle of elevation from Sarah was 48 degrees and from Amerie was 70 degrees. Draw a picture to show this situation and find the height of the aircraft, to the nearest hundredth of a foot. I have been honestly looking up youtube videos because its as if i have the line of sight, but dont know how to jump into the problem, I divided the triangle in half because i believed that each female had a line of sight different from each others, but i cannot find any youtube videos that are similar to what I am trying to solve. I dont even think it is a sas question because even if I divided something by 1-> the mile that separates the two, 1 wouldnt do anything unless I possible convert the mile into maybe centimeters, but than if I divide it into centimeters, why not into inches, or etc.
 
SO FAR IN REGARDS TO MY WIRE QUESTION I DID THE FOLLOWING: I called the point 100' from the wire A; call the the top of the tower B; I called the point where wire touches the ground C and the bottom of the tower D.

Angle ABD = 58 deg; angle CBD = 25 deg; therefore angle ABC = 33 deg.

Use law of cosines to find BC; 100 / sin 33 = BC / sin 32. So BC = 97.297 ft

Now, tan 65 deg = BD / 97.297, so BD, the height of the tower, is 88.18, or 88 feet
 
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sbeaubrun said:
A wire attached to the top of a tower makes an angle of 65 degrees with the ground. At a point on the ground 100 feet away from the end of the wire, the angle of elevation to the top will be 32 degrees. how would one find the height of the tower, to the nearest foot.
Click to expand...
The trick here is to assume that the Height is vertical Height and the distance is measured horizontally.
A right Triangle with one side h and the other side 100. tan(32) = h/100.
Look up tan and see how it is defined. You can use a calculator to calculate tan(32).
 
Law of sines

When i asked my teacher this, she stated to only focus on law of sines, nothing else
 
sbeaubrun said:
I HAVE TWO PROBLEMS THAT HAVE RACKED MY BRAIN, I MISSED ONE DAY OF SCHOOL TRYING TO GET A WISDOM TOOTH TAKEN OUT AND I HAVE BEEN LOST EVER SINCE. I HAVE AN EXAM COMING UP AND HAVE BEEN TRYING TO GET HELP BECAUSE I KNOW THESE TWO QUESTIONS IF NOT SIMILAR ONES WILL BE ON THE TEST. A FRIEND GAVE ME THE ANSWERS BUT I NEED TO UNDERSTANDDDDDD HOW TO PROPERLY SOLVE IT AND THAN MAKE SURE THAT THE ANSWER WAS EVEN CORRECT. ANY HELP YOU CAN GIVE WOULD BE AWESOME:

A wire attached to the top of a tower makes an angle of 65 degrees with the ground. At a point on the ground 100 feet away from the end of the wire, the angle of elevation to the top will be 32 degrees. how would one find the height of the tower, to the nearest foot.
Click to expand...
Yes, the sine law looks like the way to go. The wires and the ground form a triangle with two angles, of 34 and 180- 65= 115 degrees, which means that the angle between the two wires, at the top of the tower, is 180- 34- 115= 31 degrees. Use that, together with the fact that the side opposite that angle has length 100, in the sine law to find the length of the wire where the angle is 65 degrees. That will be the hypotenuse of a right triangle where the height of the tower is the "opposite side" to the 65 degree angle.


sarah and amerie were standing one mile apart on eastern parkway. they saw a jet blue aircraft between them directly above the road. The angle of elevation from Sarah was 48 degrees and from Amerie was 70 degrees. Draw a picture to show this situation and find the height of the aircraft, to the nearest hundredth of a foot. I have been honestly looking up youtube videos because its as if i have the line of sight, but dont know how to jump into the problem, I divided the triangle in half because i believed that each female had a line of sight different from each others, but i cannot find any youtube videos that are similar to what I am trying to solve. I dont even think it is a sas question because even if I divided something by 1-> the mile that separates the two, 1 wouldnt do anything unless I possible convert the mile into maybe centimeters, but than if I divide it into centimeters, why not into inches, or etc.
Click to expand...
I can't imagine why you would convert miles into any other measurement- certainly not centimeters. You can, without loss of generality, assume that Sarah, Amerie, and the point on the earth just below the jet lie on a single line- just imagine to circles centered on the point below the jet, through the two girls. Any points on those circles give the same angles and the same distances. (I used this in the previous problem without mentioning it- or even thinking about it.)

So the lines of sight of the two to the jet are sides of triangle with angles 48 and 180- 70= 110 degrees. The third angle in that right triangle is 180- 48- 78= 54 degrees. The side opposite that angle has length 1 mile so you can use the sine law to find the other two sides. The side representing the line of sight of Amerie is the hypotuse of a right triangle in which the height of the airplane is the "opposite side" to the 70 degree angle.

Now you have a triangle with
 
HallsofIvy, Now I have a triangle...? In my mind I always dud I just had 70 degrees on the left side of the triangle 48 degrees on the right, searching for the height with the number 1 (which represents the mile) below the entire triangle
 
Ok so you have a triangle with an angle of 70, a side of 1, and another angle of 48.

so the angle made by person A to the spacecraft to person B is? hint: 180-70-48=

so now use law of sines with the sin of that new angle you got, over 1

and then set it equal to say sin of 70, over "x"
x representing the side made by person B and the spacecraft.

now draw in the height

then do sin 90 over x, whatever x is, is equal to sin 48 over "y"
y representing the the height of the spacecraft.

does this help?!
 
this is what i got

180-70-48= 62
sin62= sin70
1 x
-0.74=0.77
1 x
CROSSMULTIPLY
0.77= -.074x


0.77 0.77
x= -.96


sin 90=sin 48
-.96 y
0.89= -.77
-.96 y
crossmultiply
0.89y= .74
.89 .89
y= .83 to the nearest hundredth wouldhave to be 83 feet
 
lookagain said:
** with the side for the triangles' height drawn on the left-hand side of a diagram and the women's positions drawn on the right-hand side along the largest triangle's base.
Click to expand...

The women are on opposite sides of the aircraft. And with that in mind I got 4175.98 feet for the height of the spacecraft, or those whereabouts.
 
sbeaubrun said:
180-70-48= 62
sin62= sin70
1 x
-0.74=0.77
1 x
CROSSMULTIPLY
0.77= -.074x


0.77 0.77
x= -.96


sin 90=sin 48
-.96 y
0.89= -.77
-.96 y
crossmultiply
0.89y= .74
.89 .89
y= .83 to the nearest hundredth wouldhave to be 83 feet
Click to expand...

I'm not sure how you those numbers but heres how you should have started

180-70-48=62 you got that right

law of sines

sin(62)/5280=sin(70)/x I went ahead and put miles into feet

cross multiply to get

5280*sin(70)=sin(62)*x

4961.577038=sin(62)*x It's best to round at the end (gives you more precise answers)

4961.577038/sin(62)=x

5619.333557=x this gives you the side length of the side adjacent to the 48 degree angle

now draw in a height from the aircraft, and you have two right triangles. we are going to use the one with 90, 48, 42 as the angles, ( use a picture as I explain this)

law of sines again

sin(90)/5619.333557=sin(48)/height of aircraft

cross multiply

5619.333557*sin(48)=height*sin(90)

4175.978656/sin(90)=height

sin(90) is equal to one so

4175.98=height of the aircraft (in feet)

about 0.79 miles high
 
Denis said:
Good stuff, Mack!
Next time, don't give full solution: let the OP finish up.

In this case, you could have stopped after:
"5619.333557=x this gives you the side length of the side adjacent to the 48 degree angle"
and told the OP to continue using right triangles...
Click to expand...

Ok yeah sorry!
 
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