From a point P on the …
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From a point P on the ground the angle of elevation of the top of a 10 m tall building is 30 degree. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45 degree. Find length of flagstaff and the distance of building from the point P.
Posted by ? ? 6 years, 3 months ago
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Sia ? 6 years, 3 months ago
Let height of flagstaff be BD = x m
{tex}\therefore \quad \tan 30 ^ { \circ } = \frac { A B } { A P }{/tex}
{tex}\Rightarrow \quad \frac { 1 } { \sqrt { 3 } } = \frac { 10 } { A P }{/tex}
{tex}A P = 10 \sqrt { 3 }{/tex}
distance of the building from P.
{tex}= 10 \times 1.732 = 17.32 \mathrm { m }{/tex}
{tex}\tan 45 ^ { \circ } = \frac { A D } { A P } \text { or } 1 = \frac { 10 + x } { 17 \cdot 32 }{/tex}
or, x + 10 = 17.32
x = 17.32 - 10
x = 7.32
Hence, length of flagstaff x = 1 7.32 m.
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