Answer:
382.925 feets
Step-by-step explanation:
The solution diagram is attached below :
Converting radian measurement to degree :
radian angle * 180/π = degree angle
1.2 * 180/π = 68.755°
0.9 * 180/π = 51.566°
Height of dam is h:
Using trigonometry :
Tan θ = opposite / Adjacent
Tan 68.755° = h / x
h = x Tan 68.755° - - - (1)
Tan 51.566° = h / (155+x)
h = (155+x) tan 51.566° - - - (2)
Equate (1) and (2)
x Tan 68.755 = (155+x) Tan 51.566
x Tan 68.755 = 155tan 51.566 + x tan 51.566
x Tan 68.755 = 195.32311 + x Tan 51.566
x Tan 68.755 - x Tan 51.566 = 195.32311
x(tan 68.755 - tan 51.566) = 195.32311
x * 1.3120110 = 195.32311
1.3120110x = 195.32311
x = 195.32311 / 1.3120110
x = 148.87307
Using :
h = x Tan 68.755
h = 148.87307 * tan(68.755)
h = 382.92539
h = 382.925 feets
