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Mathematics · Some Applications of Trigonometry · NCERT Examples

Example 4

A complete, independently verified solution for NCERT Example 4.

Mathematics · Chapter 9 · NCERT Examples

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NCERT Example

Example 4

flagstaff · two angles of elevation

From a point P on the ground, the angle of elevation of the top of a 10 m building is 30°. A flag is hoisted at the top and the angle of elevation of the top of the flagstaff is 45°. Find the flagstaff length and the distance of the building from P. Take √3 = 1.732.

A 10 metre building AB with flagstaff BD, viewed from point P at angles of 30 and 45 degrees.
Figure 9-7 from the supplied NCERT chapter.

Solution

Board-exam working:

Let PA be the distance from P to the building.

tan⁡30∘=ABPA\tan30^\circ=\frac{AB}{PA}
13=10PA\frac1{\sqrt3}=\frac{10}{PA}
PA=103=17.32 mPA=10\sqrt3=17.32\text{ m}

Let DB = x m be the flagstaff length. Then AD = 10 + x.

tan⁡45∘=ADPA\tan45^\circ=\frac{AD}{PA}
1=10+x1031=\frac{10+x}{10\sqrt3}
10+x=10310+x=10\sqrt3
x=10(3−1)=7.32 mx=10(\sqrt3-1)=7.32\text{ m}

Final answer

The flagstaff is 7.32 m long and the building is 17.32 m from P.