A, B, C and D are on horizontal level ground and CT is vertical pole. B is 35 m due east of C, A is 60 m South of C and D is 60 m West of A.
Calculate the angle of elevation of T from N.
I m really suck...plz help
beats me -- where is N?
From Pyth thereom,AB =root (35^2+60^2)= 5 root(193)
Height CN=AC*CB/ AB= 60*35/ 5 root(193)= 420/root(193)
Now find CT
Tan40 = CT/ DC
But DC= 60 root 2 ( it is hyp of rt triangle ADC)
CT= DC tan 40= 60 root 2 * 0.84
Angle of elevation of TN is
Arc Tan(CT/CN)= Arc tan (60 root 2 * 0.84/420/root(193))
= Arc tan ( root 386 * 0.12)
= Arc tan ( 19.65 * 0.12)
= Arc tan (2.358)
= 67.02 deg
To calculate the angle of elevation of point T from point N in this scenario, we need to use trigonometry and some basic geometry.
Let's break down the given information:
- B is 35 meters due east of C.
- A is 60 meters south of C.
- D is 60 meters west of A.
To visualize the situation, let's draw a diagram:
T
|
|
|
|
B------C-------D
|
|
|
|
A
|
|
|
N
In this diagram, CT is the vertical pole, and we need to find the angle of elevation of T from N.
To solve this problem, we will use the tangent function (tan):
Tan(angle) = Opposite / Adjacent
In this case, the opposite side is the vertical distance TC, and the adjacent side is the horizontal distance NC.
Now, let's calculate the lengths of TC and NC:
- We know that A is 60 meters south of C, and D is 60 meters west of A. Therefore, the vertical distance TC is the sum of AB and CD.
TC = AB + CD
- We need to find the lengths of AB and CD using the Pythagorean theorem:
AB = √(AC^2 - BC^2)
CD = √(AC^2 - AD^2)
- Let's substitute the given values:
BC = 35 m (given)
AC = TC + AB = TC + √(AC^2 - BC^2) = TC + √(TC^2 - BC^2) (since AB = TC)
AD = 60 m (given)
- Now, we can substitute these values into the equations for AB and CD:
AB = √((TC + √(TC^2 - BC^2))^2 - BC^2)
CD = √((TC + √(TC^2 - BC^2))^2 - AD^2)
- Simplifying and solving these equations will give us the values of AB and CD.
Finally, we can calculate the angle of elevation using the tangent function:
Angle of elevation = tan^(-1)(TC / NC)
Substitute the values of TC and NC into this equation to find the angle of elevation.