Question

Question #faf52

Answer 1

The height of the mast is `75m`
One wire is `85m` and the other is `77.7m`

Explanation:

let the base be `a`

The Sine Rule
`a/sin A = b/sin B = c/sin C`

The internal angles of a triangle always add up to `180^0`
Therefore the angle between the wires at the top of the mast, and opposite `a`, is `180^0 - 62^0 - 75^0 = 43^0`

let `b` be the length of the wire opposite the angle of `75^0`
using the Sin Rule
`60/sin 43^0 = b/sin 75^0`

Simplifying
`b = 60*(sin 75^0/sin 43^0 )= 84.979`

let `c` be the length of the wire opposite the angle of `62^0`
using the Sin Rule
`60/sin 43^0 = c/sin 62^0`

Simplifying
`b = 60*(sin 62^0/sin 43^0) = 77.679`

Heron's formula for the area of a triangle
`Area = sqrt(s(s-a)(s-b)(s-c))` where `s` is the semi-perimeter of the triangle

calculate the semi-perimeter
`s = (60+84.979+77.679)/2 = 111.329`

Substitue into Heron's formula
Area = `sqrt(111.329(111.329 - 60)(111.329 - 84.979)(111.329 - 77.679)) = 2250.963`

The area of a triangle can also be calculated as `1/2 base * height`

therefore `height = 2*(area)/(base)`
in this case
height = `2*2250.963/60 = 75.032m`