Question #faf52

1 Answer
Nov 19, 2017

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#