A ship leaves port R sails to port S and then to port T. The bearing of S from R is 112. The Bearing of T from S is 033 The distance RT is 75 km and the distance RS is 56 km
a) Draw a diagram showing the journey of the ship from R to S to T
b) calculate- i)The size of angle RST ii)The size of angle RTS iii) the bearing of R from T
c) The ship leaves port T and travels due west to a point X which is due north of R.
i) Show on your diagram the journey from T to X
ii) calculate the distance TX
PLEASE HELP ME WITH THIS ONE IT IS SUPPER IMPORTANT!!!
so, are you rachel or john?
reposting won't get you help any faster, and just wastes our time.
have you drawn the diagram?
You can see that angle RST is 91 degrees.
So, what's next?
The bearings 112° to 033°
112°+033°=145°
a) Here is a diagram of the ship's journey from port R to port S to port T:
R
\
56 \ 75
\ \
S______T
b) i) To find the angle RST, we can use the fact that the sum of the angles in a triangle is 180 degrees. So, we subtract the given angles:
angle RST = 180 - angle RTS - angle STR
angle RST = 180 - 112 - 33
angle RST = 35 degrees
ii) To find the angle RTS, we know that angle RTS is the same as angle STR, since they are opposite angles in a triangle. Therefore:
angle RTS = angle STR = 33 degrees
iii) The bearing of R from T can be found by subtracting the bearing of T from S (033) from 180 degrees, since R and T are on the opposite side of the line formed by S and T:
Bearing of R from T = 180 - 33
Bearing of R from T = 147 degrees
c) i) To show the ship's journey from T to X, we need to travel due west from T and then due north to reach X. Here is an updated diagram:
R
\
56 \ 75
\ \
S______T
|
X
ii) To calculate the distance TX, we can use the Pythagorean theorem. Since the ship travels due west, the distance TX is equal to the difference in the y-coordinates of T and X:
Distance TX = |y-coordinate of T - y-coordinate of X|
Since X is due north of R, the y-coordinate of X is the same as the y-coordinate of R. The y-coordinate of T is 0.
Distance TX = |0 - y-coordinate of R|
We are not given the coordinates of R, so we cannot calculate the exact distance TX without additional information.
a) To draw the diagram, start by drawing three points labeled R, S, and T. Place R at the origin (0,0). Based on the given information, draw a line segment from R to S with a length of 56 km. Using the bearing of S from R (112 degrees), draw a line segment from S to represent the direction. From S, draw another line segment based on the given bearing of T from S (33 degrees). Finally, label the lengths of the segments RT (75 km) and RS (56 km) on the diagram.
b) i) To find the size of angle RST, use the Law of Cosines. In triangle RST, we have the lengths RT (75 km), RS (56 km), and the included angle at S (33 degrees). The formula for the Law of Cosines is:
RT² = RS² + ST² - 2(RS)(ST)cos(angle RST)
Plug in the known values:
75² = 56² + ST² - 2(56)(ST)cos(33°)
Solve for ST:
ST² - 2(56)(ST)cos(33°) + 56² - 75² = 0
Solve the quadratic equation to find ST. The positive solution will give the distance ST. Once you have ST, you can use the Law of Sines to find angle RST. The formula for the Law of Sines is:
sin(angle RST) / ST = sin(angle RTS) / RT
ii) To find the size of angle RTS, use the Law of Sines. From the Law of Sines, we have:
sin(angle RTS) / RT = sin(angle RST) / ST
Solve for angle RTS by substituting the known values.
iii) To find the bearing of R from T, subtract the angle RTS from 180 degrees (since bearings use the direction measured clockwise from the north).