Question

the angle of elevation from the top of the tower from a point 100m away from the ground is fourty five degrees. what is the hieght of the tower in the nearest meter​

Answer 1

`\Huge \boxed{\mathrm{100 \ meters}}`

Explanation:

The base of the right triangle created is 100 meters.

The angle between the base and the hypotenuse of the right triangle is 45 degrees.

We can use trigonometric functions to solve for the height of the tower.

`\displaystyle \mathrm{tan(\theta)=(opposite)/(adjacent) }`

Let the height be x.

`\displaystyle \mathrm{tan(45)}=(x)/(100)`

Multiplying both sides by 100.

`\displaystyle 100 \cdot \mathrm{tan(45)}=x`

`100=x`

The height of the tower is 100 meters.

Answer 2

100m

Explanation:

x=the height of the tower

100m=the distance from the tower

45 degrees the angle of elevation

Drawing a diagram allows you to see that you can form a 'right-angled triangle'.

Using trig. :

Tan 45=x/100m

multiply both sides by 100m

100m*tan 45=100m