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The length of the shadow of a pole inclined at 10°to the vertical towards the sun is 2.05 metres,when the elevation of the sun is 38° .Find the length of the pole.

Asked by agarrajeev06 11th January 2019, 3:08 PM
Answered by Expert

Figure shows a pole AB of length l which is inclined at 10° to the vertical, casting shadow AO of length 2.05 m,
when the elevation of sun is at 38°
From ΔACO, we have h = 2.05×tan38° = 2.05×0.78 ≈ 1.60 m
From ΔBCD, we have   begin mathsize 12px style fraction numerator l space sin 10 over denominator open parentheses l space cos 10 minus h close parentheses end fraction space equals space tan 52 space almost equal to space 1.28 end style
hence begin mathsize 12px style fraction numerator l cross times 0.174 over denominator l cross times 0.985 space minus space 1.6 end fraction space equals space 1.28 end style
solving the above equation for l, we get l = 1.88 m.
Answered by Expert 14th January 2019, 4:01 PM
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