An electric pole is 10 m high. A steel wire tied to the top of the pole is affixed at a point on the ground to keep the pole upright. If the wire makes an angle of $45^o$ with the horizontal through the foot of the pole, find the length of the wire.
VerifiedHint: The angle of elevation is the angle above the eye level of the observer towards a given point. The angle of depression is the angle below the eye level of the observer towards a given point. The sine function is the ratio of the opposite side and the hypotenuse.
Complete step-by-step answer:
Let the steel wire DE be of the length h. The height of the electric pole CD is 10 m. It is given that the wire ED makes an angle of $45^o$ with the horizontal.
We will apply trigonometric formulas in triangle DCE as follows-
\[ In\;\vartriangle DCE,\; \]
\[ \sin {45^{\text{o}}} = \dfrac{{CD}}{{ED}} \]
\[ \dfrac{1}{{\sqrt 2 }} = \dfrac{{10}}{{DE}} \]
\[ DE = 10\sqrt 2 {\text{m}} \]
This is the length of the steel wire and the required answer.
Note: In such types of questions, it is important to read the language of the question carefully and draw the diagram step by step correctly. When the diagram is drawn, we just have to apply basic trigonometry to find the required answer.
