A support wire to the top of a newly planted tree is 15 m 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 45 degrees to the ground. Determine an exact expression for the distance between the points where the two support wires are attached to the ground.
I tried this question and got 2.0 metres. Is this correct?
That's not what I get. I get (15/2)(√3-1)
How did you get your answer (which is not exact, by the way)?
how did u get your answer?
How did you get your answer please tell me
A better question might be how did you get yours? Did you draw a diagram? since sin(30) = 1/2, the pole is 15/2 meters tall.
A 45-45-90 triangle has equal legs, so base of the 2nd wire is 15/2 meters from the pole.
I'll leave the rest to you. The Pythagorean Theorem should help.
Same question as above. Steve got the answer correct, but I'm having trouble laying it out with the diagram. Any one willing to walk this through with me step by step in a tutoring way? I want to learn not just have an answer. Thanks
To determine the exact expression for the distance between the points where the two support wires are attached to the ground, we can use trigonometry.
Let's visualize the situation. We have a tree with two support wires attached to its top. The first wire forms an angle of 30 degrees with the ground, and the second wire forms an angle of 45 degrees with the ground. The length of the first wire is 15 meters.
First, let's find the height of the tree using the first wire. We can use the trigonometric function sine, as it relates the opposite side (height) to the hypotenuse (length of the wire).
sin(30 degrees) = opposite / hypotenuse
sin(30 degrees) = height / 15 meters
Now, we know that the sine of 30 degrees is equal to 0.5, so we can substitute:
0.5 = height / 15 meters
Solving for the height:
height = 0.5 * 15 meters
height = 7.5 meters
The height of the tree is 7.5 meters.
Next, let's find the distance on the ground between the points where the wires are attached. Since both wires are attached to the top of the tree, we can consider the point where the first wire is attached as the origin, (0,0), on a coordinate system.
The distance between the two points can be found by determining the horizontal distance covered by each wire.
For the first wire (forming a 30-degree angle with the ground):
cos(30 degrees) = adjacent / hypotenuse
cos(30 degrees) = distance / 15 meters
The cosine of 30 degrees is equal to √3/2, so we can substitute:
√3/2 = distance / 15 meters
Solving for the distance:
distance = (√3/2) * 15 meters
distance = (15√3) / 2 meters
distance ≈ 12.99 meters (rounded to two decimal places)
Therefore, the exact expression for the distance between the points where the two support wires are attached to the ground is (15√3) / 2 meters, which is approximately 12.99 meters.
Your answer of 2.0 meters is incorrect. The correct answer is approximately 12.99 meters.