Here's a problem:
A support wire to the top of a newly planted tree is 20m long. It forms an angle of 30 degrees to the ground. On the same side of the tree, a second wire is also attached to the top of the tree, but it makes an angle of 60 degrees to the ground.
Determine an exact expression for the distance between the points where the two support wires are attached to the ground.
And here's another one I'm having trouble with:
To get to Paul's house, Jen leaves her house travelling at 50 km/h along a road in an easterly direction for 45 min. She then takes a 30 degree right turn onto a second road and travels at 60 km/h for 30 min before arriving at Paul's house.
Determine an exact expression for the distance between the two houses.
Any help at all would be very much appreciated.
A support wire to the top of a newly planted tree is 20m long. It forms an angle of 30 degrees to the ground. On the same side of the tree, a second wire is also attached to the top of the tree, but it makes an angle of 60 degrees to the ground.
Determine an exact expression for the distance between the points where the two support wires are attached to the ground.
And here's another one I'm having trouble with:
To get to Paul's house, Jen leaves her house travelling at 50 km/h along a road in an easterly direction for 45 min. She then takes a 30 degree right turn onto a second road and travels at 60 km/h for 30 min before arriving at Paul's house.
Determine an exact expression for the distance between the two houses.
Any help at all would be very much appreciated.
-
let x = distance from second wire ground point to tree base
First wire
sin30 degrees = tree height/20
tree height = 20*sin30
distance to base of tree = 20*cos 30 = 17.32m
---------------
second wire
distance to base of tree x
tan60 = (20*sin30)/x
1.732 = 20*0.5/x
x = 10/1.732= 5.77m
Distance between two ground attachment points = 17.32 - 5.77 = 11.55m
--------------------------------------…
First wire
sin30 degrees = tree height/20
tree height = 20*sin30
distance to base of tree = 20*cos 30 = 17.32m
---------------
second wire
distance to base of tree x
tan60 = (20*sin30)/x
1.732 = 20*0.5/x
x = 10/1.732= 5.77m
Distance between two ground attachment points = 17.32 - 5.77 = 11.55m
--------------------------------------…
-
Draw them out to help. This is a triangle problem and I don't have my scientific calculator with me to make math easy. But the first problem as you should've been aware of is a 30-60-90 triangle. Which makes it easier. But I'm not sure which leg is the longer leg...... If 20m is the shorter than that hypotenuse (a.k.a. distance between the 2 wires) should be 40m. [If it's the other leg. Then the hyp. is 20 on the square root of 3.] Most likely though they want 40m.
THe next problem I'm going to pretend it is also a right triangle though assuming in math is horrible. (As I said no calculator to make sure it is indeed a right triangle). The first bit of the trip is 11250km. Hard to explain it well. (I changed it to km/m by multiply 50 by 60. so 3000/60m. divided both by 12 because 60/5 is 12 and 5 is a common variable of both 45 and 50. getting 250km/m. then multiply by 45.) Hope that made sense. But then do the same for the other side. Find which is the hyp. and use Pythagoreanm theorem.
Hope I helped. Sorry for not doing the last of the 2nd problem my brain is tired.
THe next problem I'm going to pretend it is also a right triangle though assuming in math is horrible. (As I said no calculator to make sure it is indeed a right triangle). The first bit of the trip is 11250km. Hard to explain it well. (I changed it to km/m by multiply 50 by 60. so 3000/60m. divided both by 12 because 60/5 is 12 and 5 is a common variable of both 45 and 50. getting 250km/m. then multiply by 45.) Hope that made sense. But then do the same for the other side. Find which is the hyp. and use Pythagoreanm theorem.
Hope I helped. Sorry for not doing the last of the 2nd problem my brain is tired.