Question

A circus artist is climbing through a 15 m long rope which is highly stretched and tied from the top of a vertical pole to the ground as show below. Based on the above information, answer the following questions. i. If the angle made by the rope to the ground level is 45, then find the distance between artist and pole at ground level ii. Find the height of the pole angle made by the rope to the ground level is 30.​

Answer 1

Answer:

Let AB be the vertical pole and CA be the rope. Then,

∠ACB=30

o

and AC=20 m

In right △ ABC,

sin30

o

=

AC

AB

2

1

=

20

AB

AB=10 m

Therefore, the height of the pole is 10 m.

solution

Answer 2

Answer:

(i) distance between pole and artist at ground level = 10.6 m

(ii) height of the pole = 7.5 m

Step-by-step explanation:

length of rope = 15 m

(i) given, angle made by rope to the ground is 45°

to find: distance between pole and artist at ground level

cos 45 = $\frac{QR}{PQ}$

$\frac{1}{\sqrt{2} }$ = $\frac{QR}{15}$

QR = $\frac{15}{\sqrt{2} }$

QR = 10.6 m

therefore, distance between pole and artist at ground level = 10.6 m

(ii) given, angle made by rope to the ground is 30°

to find: height of the pole

sin 30 = $\frac{PR}{PQ}$

$\frac{1}{2}=\frac{PR}{15}$

PR = $\frac{15}{2}$

= 7.5 m

therefore, height of the pole = 7.5 m

refer to the image attached