P is a point 2m above the ground and 15m away from a tower. The angle of elevation of the tower from P is 65 degrees. Calculate the height of the tower.
If the base of the tower is on the same horizontal plane as the point 2m below P, then
(h-2)/15= tan65
h=2+15tan65
To calculate the height of the tower, we can use trigonometry and the concept of similar triangles.
Let's first draw a diagram to visualize the situation:
P
/
/
/|
65°/
/
/|
Tower /
In this diagram, P represents the point 2m above the ground and 15m away from the tower. The angle of elevation from P to the top of the tower is 65 degrees.
Now, let's define some variables:
- Let h be the height of the tower.
- Let d be the distance from the base of the tower to point P.
In this case, we know that the angle of elevation, the height of point P, and the distance from the tower to point P form a right triangle. So, we can use the tangent function to find the height of the tower.
The tangent of an angle is defined as the ratio between the opposite side and the adjacent side of a right triangle. In this case, the height h of the tower is the opposite side, and the distance d is the adjacent side.
Using the formula for the tangent function, we have:
Tan(65°) = h / d
Now, substitute the known values:
Tan(65°) = h / 15m
To find the value of the tangent of 65 degrees, you can use a scientific calculator or look it up in a trigonometric table.
Let's assume that the tangent of 65 degrees is approximately 2.1445. We can then rearrange the equation:
2.1445 = h / 15m
Multiply both sides of the equation by 15m:
2.1445 * 15m = h
h ≈ 32.17m
Therefore, the height of the tower is approximately 32.17 meters.