Question

The angle of elevation of the top of a tower from a point 100m away is 45 degrees. What is the height of the tower to the nearest metres?

Answer 1

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

Step-by-step 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) }`

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

Multiplying both sides by 100.

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

`\displaystyle \mathrm{100 }= x`

The height of the tower is 100 meters.

Answer 2

Answer: 100 meters

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Step-by-step explanation:

If you draw out the diagram, then you'll find that a 45-45-90 triangle forms. The nice thing about this type of triangle is that the two legs are always the same length. The horizontal leg is 100 meters, so the vertical leg must also be 100 meters.

Side note: this type of triangle is an isosceles right triangle.

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You could use the tangent rule to get the same thing

tan(angle) = opposite/adjacent

tan(45) = 100/x

1 = 100/x

1*x = 100

x = 100

In this case, the opposite leg is the vertical leg since it is furthest from the angle of elevation.