The angle of elevation of the top of vertical tower from a point on the ground 60. From another point 10m vertically above the first , its angle of elevation 45. Find the height of the tower.
To solve this problem, let's break it down into two parts:
Part 1: Finding the distance from the second point to the tower's base.
Let's denote the distance from the first point (on the ground) to the tower's base as "x."
We have the following information:
- Angle of elevation from the first point to the top of the tower: 60 degrees.
- Distance from the second point (which is 10m vertically above the first point) to the tower's base: x meters.
Using trigonometry, we can relate these given values:
tan(60) = height of the tower / x
From the given information, we know that tan(60) = √3.
Thus, we get:
√3 = height of the tower / x
Solving for x, we have:
x = height of the tower / √3
Part 2: Finding the height of the tower.
Let's denote the height of the tower as "h."
Now, consider the information given for the second point:
- Angle of elevation from the second point to the top of the tower: 45 degrees.
- Distance from the second point to the tower's base: x meters (as derived in Part 1).
Using trigonometry again, we can relate these given values:
tan(45) = h / (x + 10)
From the given information, we know that tan(45) = 1.
Thus, we get:
1 = h / (x + 10)
Rearranging the equation, we have:
h = x + 10
Now, substitute the value of x found in Part 1 into this equation:
h = (height of the tower / √3) + 10
Therefore, the height of the tower can be found using this equation. Plug in the appropriate values to get the final answer.
It's so hard
for the first point you have
tan(60) = height/adjacent
for the second point you have
tan(45) = (height - 10m)/adjacent
so height/tan(60) = (height - 10m)/tan(45)
put in the values for each tangent and solve for height