How can find the height of a tower?

Question

It is a 10th stanadered math question. Pls explain with example.

Answer 1

There are a few ways:

1) Use A squared + B squared = C squared.
Example: If you have A and that is the distance from you to the building and C, the hypotenus of the triangle created; square A and subtract it from whatever C squared is. Then take the square root of that answer and you have B for the height of the tower.

2) Do law of Sines: Take the sine of the angle and put it over X, set it equal to the sine of 90 over the length of the hypotenus. The 90 is for the right angle created by the tower and ground. Then you cross multiply, putting X with the sine of 90. In corilation put the length of the hypotenus with the the sine of the angle across from X. Divide by the sine of 90 to cancel it out and seperate X from the rest of the equation. Also divide the other side by the sine of 90 because what you do to one side you do to the other. Solve it out on a calculator (scientific or graphing so that you have the sin, cos, tan buttons) and you have X, standing for the height of the tower.

3) Law of Cosines: This one gets complicated unless you can write it out in equation formula. You take X, the tower you are trying to solve for and have the other two lengths and the angle across from your tower. The equation is X squared = g (ground side) squared + h (hypotenus) squared - 2(g)(h)cos(x)<-- [the angle across from the tower] all over 2(g)(h). From there you take the square root of the number you came up with, making sure that your calculator is in Radians instead of degrees. And you have X, the height of your tower.

Hope you can get something to work out from that!

Answer 2

Usually, this type of question is encountered in algebra or trigonometry. What information do you know? Do you have the angle of elevation and the distance from the foot of the tower? (1) Do you have the height of an object, the length of its shadow, and the length of the tower's shadow? (2) Do you have the height an object that when looked at it appears the top of the object and the top of the tower match up, the distance to the object, and the distance to the tower? (3)

(1) This is a trig question. The height of a tower is measured perpendicular to the ground, so you will be forming a right angle at the base of the tower. Since the tangent function relates an angle to the ratio of the side opposite the angle and the side adjacent the angle, the height of the tower is equal to the length of the adjacent side (distance to the tower) times the tangent of the angle of elevation.
(2) This is a proportion question. Within an acceptable margin of error, the rays of the sun are striking both objects from the same elevation, so the ratio of the height of the object to the object's shadow is equal to the ratio of the height of the tower to the tower's shadow; or, the tower's height equals the object's height times the length of the tower's shadow divided by the lenght of the object's shadow.
(3) This is also a proportion by similar triangles, and follows similarly to (2). The tower's height equals the height of the object times the distance to the tower divided by the distance to the object.

If you have different information, then you may need to use a different method not mentioned here.

Answer 3

There's an old joke. How can you use a barometer to determine the height of a tower?
> drop the barometer from the top and measure the time it takes to fall
> find the custodian and give him the barometer in exchange for the height of the tower
> use the change in pressure measured by the barometer to determine the height

As for your tower:
> select a distance from the tower and measure the angle, then use the tangent
> Take a barometer and use the change in air pressure between the top and bottom to figure out the barometric height
> Take GPS receiver and collect data and the base and at the top and take the difference in heights
> Get a long rope
> Drop a lead fishing weight and measure the time it takes to fall, use 1/2gt^2 to determine the distance

Answer 4

you can drop something from it. the time, t, for the object to hit the ground is used to calculate the height. the height h of the tower is given by
h=16 t^2, where t is in seconds and height is in feet

hence if it took 3 seconds, the height would be
h= 16 * 3^2 or
h= 16*9
h= 144 feet

you can also measure the shadow, and compare it to the length of a shadow of an object of known height.

set up a proportion...

known object height/shadow length = tower height/tower shadow length

you will know 3 of the four numbers.... solve for the 4th. :-).

Answer 5

use a protactor to measure the angle that tower makes with the point from where u r standing. then from the same point calculate the distance of foot of the tower, now apply trignometry and use tanQ= perp.\ base and put the values to get the perp. dist. i.e. the height.

Answer 6

use trigonometry

find the angle with a protractor then measure how far you stand from the building