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

Question

Marlene Broomfield · Accepted 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
$∠ O A B = 41^{\circ}$
$∠ O B A = 90^{\circ}$
$A B = 34 f t$
length of wire 1= OA
Step2
Part A
To calculate the length of pole,
In $△ O A B$ ,
$\frac{P e r p e n d i c u l a r}{B a s e} = \tan (41^{\circ})$
$\frac{O B}{A B} = \tan (41^{\circ})$
$O B = A B \times \tan (41^{\circ})$
$= 34 \times \tan (41^{\circ})$
$= 29.56 f t$
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 $△ O A B$ ,
${(O A)}^{2} = {(O B)}^{2} + {(A B)}^{2}$
$= {(29.56)}^{2} + {(34)}^{2}$
$= 873.7936 + 1156$
${(O A)}^{2} = 2029.7936$
$O A = \sqrt{2029.7936}$
$O A = 45.05 f t$
Hence wire 1 is 45.05 ft long

A pole has two wires attached to it, one on

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