A pole has two wires attached to it, one on each side, forming two right triangles as shown.

1 Answers

Best Answer

Step 1
Given that:
A pole has two wires attached to it, one on side forming two right triangles as shown,
From the figure,
Length of pole = OB
∠ OAB = 41°
∠ OBA = 90°
AB = 34 ft
length of wire 1= OA
Step2
Part A
To calculate the length of pole,
In △ OAB,
(Perpendicular)/(Base) =tan (41°)
(OB)/(AB) = tan (41°)
OB = AB * tan(41°)
=34 * tan (41°)
= 29.56 ft
Hence the poll is 29.56 ft tall
Step3
Part B
To calculate the length of wire 1,
Apply Pythagoras theorem in triangle OAB,
In △ OAB,
(OA)^(2) = (OB)^(2) + (AB)^(2)
=(29.56)^(2) +(34)^(2)
= 873.7936 + 1156
(OA)^(2) = 2029.7936
OA =sqrt(2029.7936)
OA = 45.05 ft
Hence wire 1 is 45.05 ft long