Two surveyors are on opposites sides of a swamp. To find the distance between them, one surveyor locates a point T that is 200 meters from her location at pont p. The angle of sight from T to the other surveyor's position, R, measure 72 degrees for angle RPT and 63 degrees for angle PTR. how far apart are the surveyors?
sin 63 degrees/200m= sin 45 degrees/ R
R= sin 45 degrees x 200m/sin 63 degrees
= 158.7m
No, you have done the law of sines wrong>
SinA/a=SinB/b
You have the sides mixed up.
Sin63/R=Sin45/200
check my thinking.
To find the distance between the two surveyors, we can use trigonometry. Let's break down the problem and solve it step by step:
1. Draw a diagram: Draw a diagram to visualize the problem. Label the points P, T, and R as given in the question.
T
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P------------------------R
2. Identify given information: From the problem, we know that the distance between the surveyor's location at point P and point T is 200 meters. We also know the angles of sight between the points, which are 72 degrees for angle RPT and 63 degrees for angle PTR.
3. Break down the problem: We can break down the distance between the surveyors into two components - PT and TR. We need to find out these individual distances and then add them together to get the total distance.
4. Determine PT: To find PT, we can use the concept of trigonometry. The tangent function is useful here since we have the opposite side (PT) and the adjacent side (TP).
tan(RPT) = PT / TP
We know that tan(72 degrees) = PT / 200 meters, since TP of 200 meters was given.
Now we can solve this equation to find PT:
PT = tan(72 degrees) * 200 meters
5. Determine TR: Similarly, we can use the trigonometric function tangent to find TR. The angle PTR is given as 63 degrees, and we have the opposite side (TR) and the adjacent side (TP).
tan(PTR) = TR / TP
We know that tan(63 degrees) = TR / 200 meters, since TP of 200 meters was given.
Now we can solve this equation to find TR:
TR = tan(63 degrees) * 200 meters
6. Calculate the total distance: To find the total distance between the surveyors, we add PT and TR:
Total distance = PT + TR
Now, you can calculate PT and TR using the tangent function and then add them to find the total distance between the surveyors.
The third angle of the triangle is
PRT = 180-63-72 = 45 degrees. The side with length 200 m is opposite this angle. Use the law of sines for the other side lengths.