Question

erefore, the width of the river is
he river is 3(+3 + 1).
EXERCISE 9.1
1. A circus artist is climbing a 20 m long rope, which is
tightly stretched and tied from the top of a vertical
pole to the ground. Find the height of the pole, if
the angle made by the rope with the ground level is
30° (see Fig. 9.11).​

Answer 1

Gɪᴠᴇɴ:

• A circus artist is climbing a 20m long rope.
• Angle made by the rope with ground level is 30°.

ᴛᴏ ғɪɴᴅ:

• The height of the pole.
• Distance of rope from base of the pole.

ᴀɴsᴡᴇʀ:

For figure refer to attachment:

Given that a circus artist is climbing a 20m long rope and angle made by the rope with ground level is 30°.

If we consider a right ∆ ABC right angled at B , then

• The length of rope will be hypotenuse.
• Distance of rope from pole will be base.
• Height of pole will be perpendicular.

As here base and hypotenuse are given we must use cosine.

→In ∆ ABC :

⇒cos30° = AB/AC.

⇒√3/2 = AB/ 30m.

⇒AB = 30 × √3/2 m.

⇒AB = 15√3m.

Hence the distance of rope From base of pole is 15√3m

___________________________________

As here perpendicular and hypotenuse are given we must use cosine.

→ Again in ∆ ABC :

⇒ sin30° = BC/AC.

⇒1/√2 = BC/30m.

⇒BC = 30 × 1/√2m.

⇒BC = √2×√2×15/√2 m.

⇒BC = 15√2m.

Hence the height of the pole is 15√2m.