# Geometry

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. 👍
2. 👎
3. 👁
1. Hmmm... Strange labeling. Still, using the acute angles, I get that the distance d can be found using

d cot30˚ - d cot70˚ = 75
so,
d = 75/(cot30˚ - cot70˚)

1. 👍
2. 👎
2. 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 ......

1. 👍
2. 👎
3. 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.

1. 👍
2. 👎
4. 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

1. 👍
2. 👎
5. i wanna kiss you and give you money annee i love u girl

1. 👍
2. 👎
6. I Gotchu

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.

1. 👍
2. 👎
7. I wanna know where you got the 80 from

1. 👍
2. 👎
8. Or I might just have a different question

1. 👍
2. 👎
9. 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

1. 👍
2. 👎
10. Annie really said "amosc" lol. Ty for the answers, appreciate it.

1. 👍
2. 👎

## Similar Questions

1. ### physics

You want to swim straight across a river that is 76m wide. You find that you can do this if you swim 28 degrees upstream at a constant rate of 1.7m/s relative to water. At what rate does the river flow? The angle is measure from

2. ### Math

A surveyor sights two signs and the angle between the two lines of sight measures 55. If the first and the second signs are 70 m and 50 m away,respectively,from the surveyor, find the distance between the two signs .Express your

3. ### trigonometry

A surveyor wishes to calculate the distance between the two trees B and C across a river from where he is standing. If the distance from his position, A to B is 70 meters, the distance from C to A is 100 m,and the angle of A is

4. ### Physics

A surveyor measures the distance across a straight river by the following methods: Starting directly across from a tree on the opposite bank, she walks 249 m along the river bank to establish a baseline. Then she sights across to

1. ### Calculus

An oil refinery is located on the north bank of a straight river that is 2 km wide. A pipeline is to be constructed from the refinery to storage tanks located on the south bank of the river 4 km east of the refinery. The cost of

2. ### Mathematics

An oil refinery is located on the north bank of a straight river that is 2 km wide. A pipeline is to be constructed from the refinery to storage tanks located on the south bank of the river 6 km east of the refinery. The cost of

3. ### Math

A biologist wants to know the width w of a river so that instruments for studying the pollutants in the water can be set properly. From point A, the biologist walks downstream 100 feet and sights to point C. From the sighting, it

4. ### trigonometry

. A surveyor wishes to measure the distance across Pasig River. She sets up her transit at a point C on the bank of the river, and sights on a point B on the other bank directly opposite her. Then she turns the transit through a

1. ### Math

A camper wants to know the width of a river. From point A, he walks downstream 100 feet to point B and sights a canoe across the river. It is determined that = 42°. About how wide is the river?

2. ### Pre-calculus

A surveyor standing 62 meters from the base of a building measures the angle to the top of the building and finds it to be 38°. The surveyor then measures the angle to the top of the radio tower on the building and finds that it

3. ### Inverse Functions

A surveyor is standing 550 feet from the base of a redwood tree in the California Redwood Forest. The tree is 362 feet tall. Sketch a drawing that models the situation and then find the angle of elevation of the top of the tree

4. ### Math

An oil refinery is located 1 km north of the north bank of a straight river that is 3 km wide. A pipeline is to be constructed from the refinery to storage tanks located on the south bank of the river 8 km east of the refinery.