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PSYCHO15rus [73]
3 years ago
10

The vertical angle to the top of a flagpole from point A on the ground is observed to be 37°11'. The observer walks 17 m directl

y away from point A and the flagpole to point B and finds the new angle to be 25°43'. What is the approximate height of the flagpole?

Mathematics
1 answer:
inysia [295]3 years ago
3 0

Answer:

22m

Step-by-step explanation:

Let height of flagpole=h

AB==17 m

\angle CAD=37^{\circ}11'=37+\frac{11}{60}=37.183^{\circ}(1 degree= 60 minute)

\angle B=25^{\circ}43'=25+\frac{43}{60}=25.72^{\circ}

We have to find the approximate height of the flagpole.

In triangle CDA,

\frac{CD}{DA}=tan\theta=\frac{Perpendicular\;side}{Base}

\frac{h}{DA}=tan37.183^{\circ}

h=DA(0.759)

In triangle CDB,

tan 25.72^{\circ}=\frac{CD}{DB}

0.482=\frac{h}{DA+17}

0.482DA+8.194=h

Substitute the value

0.482DA+8.194=0.759DA

8.194=0.759DA-0.482DA

8.194=0.277DA

DA=\frac{8.194}{0.277}=29.58

Substitute the value

h=29.58 \times 0.759=22.45 m\approx 22m

Hence, the height of the flagpole=22 m

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