SOLUTION: A surveyor at point A, measures the horizontal angle between a marker at point B (Further along his/her side of the river) and a tower on the opposite side of the river as 62 degre
Algebra.Com
Question 1151057: A surveyor at point A, measures the horizontal angle between a marker at point B (Further along his/her side of the river) and a tower on the opposite side of the river as 62 degrees. He/she walks 50m directly to point B where he/she measures the angle between point A and the tower to be 45 degrees.
Draw a clearly labelled diagram showing this information and use it to calculate the distances between the tower and the two observation points.
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Diagram:
Points A and B are on the same side of the river. Point C is the tower's location on the opposite side of the river.
Side lengths:
a = unknown (this side is opposite angle A)
b = unknown (this side is opposite angle B)
c = 50 (this side is opposite angle C)
Angles:
A = 62
B = 45
C = 73
Angles A and B are given in the instructions.
Angle C can be found by solving A+B+C = 180.
Equivalently, C = 180-A-B.
Note how: A+B+C = 62+45+73 = 180.
The goal is to find the side lengths a and b.
Use the law of sines to solve for side a
a/sin(A) = c/sin(C)
a/sin(62) = 50/sin(73)
a = sin(62)*50/sin(73)
a = 46.1645509631375
a = 46.16455
Use the law of sines to solve for side b
b/sin(B) = c/sin(C)
b/sin(45) = 50/sin(73)
b = sin(45)*50/sin(73)
b = 36.9707866021467
b = 36.97079
Here is the updated picture of the solved triangle
The phrase "solve a triangle" basically means "find all three angle measures and all three side lengths".
All side lengths are in meters. The values for a and b are approximate.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
first find the length of and :
......since
......since
.........≈
then,
=>
the distances between the tower and the two observation points:
the distance :
->the distance between the tower and the observation point
->the distance between the tower and the observation point
RELATED QUESTIONS
a surveyor wishes to find the distance between two in accessible points A & B on opposite (answered by jsmallt9)
a surveyor wishes to find the distance between two inaccessible points A&B on opposite... (answered by jsmallt9)
Hello, I really need your help, math is not my greatest subject. I am in college physics... (answered by ankor@dixie-net.com)
Two surveyors are on the opposite sides of a swamp. To find the distance between them,... (answered by psbhowmick)
a surveyor has measured a distance b=20m between points A and C on a river bank, as shown (answered by Boreal)
To whom may it concern,
I have trouble to do this question.
To find the width of a... (answered by Earlsdon)
To determine the width of a chasm, a marker (A) is placed directly opposite a rock (R) on (answered by MathLover1)
To determine the width of a chasm, a marker (A) is placed directly opposite a rock (R) on (answered by MowMow)
Two points A and B lie on opposite sides of a river. Another point C is located on the... (answered by Fombitz)