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