Question

a wire extends from a building at a point 18 meters up and makes a 65 angle with the ground. What is the length of the wire to the nearest hundredth of a meter?​

Answer 1

`19.86m` to the nearest hundredth.

Explanation:

The building, the wire and the ground creates a right triangle.

The point 18 meters up the building is the side opposite to the 65 degree angle.

We can use the sine ratio to find the value of the length of the wire which is the hypotenuse.

Let, the length of the wire be
`l` units.

`\sin 65\degree=(Opposite)/(Hypotenuse)`

`\sin 65\degree=(18)/(l)`

`l=(18)/(\sin 65\degree)`

`l=19.86m` to the nearest hundredth.

Answer 2

The length of the wire is 19.86 meters

Explanation:

We can find the length of the cable using a right triangle like the one shown in the figure.

In this triangle, the opposite side of the 65 ° angle represents the height from the start of the cable to the end point. If we call b to this opposite side, then:

`b = 18\ m`

The length of the cable is the hypotenuse h of this triangle

We know that by definition the sine of an angle is:

`sin(a) = (opposite)/(hypotenuse)`

So:

`sin(65\°) = (18)/(h)\\\\h = (18)/(sin (65\°))\\\\h = 19.86\ m`