A surveyor sights the far bank of a river at an angle of 110˚ to the near bank. She then moves 75 feet upriver and sights the same point on the far bank of the river at an angle of 150˚. What is the shortest distance across the river?
1.) B - 96.68
2.) B - 58.34 ft
3.) B - 39
4.) D - 48.4
5.) D - 70.0
6.) B - 95
7.) C - 169.3 ft
8.) *not sure if this is correct*
sin10 = AB/x
0.1736 = 500/x
x = 500/0.1736
x = 2880.18
amosc :) - annee-mrie
i wanna kiss you and give you money annee i love u girl
Yea I was right. It is a different question. For honors only I think. I put;
cos(10) = 500/x
x = 500/cos(10)
x = 507.7
I Gotchu
All your answers are correct.
But the last one is not. The correct answer and work would be
Cos 80 = 500/x
x = 500/cos 80
x = 2879.4 meters
This work is from brainly, I wish it would allow me to put the link,
But is doesn't. Good luck on everyone's quiz.
Annie really said "amosc" lol. Ty for the answers, appreciate it.
On my sketch I assumed the two sides of the river are parallel.
I labeled the original position as B and the second position as A
AB = 75
I labelled the reference point on the opposite side as P
I also labelled PC as the perpendicular distance between the 2 sides
angle ABP = 110°
exterior angle A = 150°
So, BAP = 30° and angle APB = 40°
in triangle ABP, using the sine law:
BP/sin30 = 75/sin40
BP = 75sin30/sin40 = ....
Now in the right-angled triangle BCP
sin70° = CP/BP
CP = BPsin70, but you know BP, so ......
Tan110 = d/X.
d = x*Tan110.
.
Tan150 = d/(x-75).
d = (x-75)*Tan150.
x*Tan110 = (x-75)*Tan150.
x = (x-75)*Tan150/Tan110,
x = (x-75)*0.21,
x = 0.21x - 15.75,
X = -20 Ft.
d = x*Tan110 = -20*Tan110 = 55 Ft.
I wanna know where you got the 80 from
Or I might just have a different question
@ ...
He got 80 degrees from the already given angle, 90 degrees.
Let me explain
If you know what the triangle looks like already, then we're only given the adjacent and opposite sides, the hypotenuse is x, which is what we're missing. The triangle is obviously a right angle, meaning we are given a 90 degree angle. 80 degrees comes from finding the angle at the top of the triangle, to which you would do (90-10 = 80). This seems a bit far out there, but this is how my teacher showed me how to do it.
So then you complete the set up
cos(80) = 500/x
multiply both sides by x, then with that answer you divide both sides by cos(80), and your sum after that is what you put into a calculator to get the final answer, which should be 2879.4 meters :thumbsup: