Question

Hey genius can uh help to solve this question



Two pillars of equal heighi, stand on either side of a roadway which is 150 m wide. From
a point on the roadway between the pillars, the elevations of the top of the pillars are 00
and 30" Find the height of the pillars and the position of the point. Use V3 = 1.73]
39. In umbrella has 8 ribs which are cqually spaced, as shown in the figure. Assuming the
umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive
ribs of the umbrella


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Answer 1

Answer:

the answer for the first question is :

height = 64.875 m

distance of the first pillar from the point is 37.5 m. and the second pillar is 112.5 m far from the point

the answer for the second question is 795.53 cm

Answer 2

Question:

Two pillars of equal heighi, stand on either side of a roadway which is 150 m wide. From a point on the roadway between the pillars, the elevations of the top of the pillars are 60° and 30°. Find the height of the pillars and the position of the point. Use √3 = 1.73]

Solution:

[ Refer the attachment for figure ]

In ∆ABC

→ tan 30° = AB/BC

→ √3 = AB/BC

→ BC = AB/√3 ...(1)

Similarly, In ∆EDC

→ tan 60° = ED/CD

→ 1/√3 = ED/CD

→ CD = ED√3

Now,

BD = 150 m (given)

We can write BD as BC + CD

So,

→ BD = BC + CD

→ 150 = AB/√3 + ED√3

→ 150 = (AB + ED√3√3)/√3

→ 150 = (AB + 3ED)/√3

→ 150√3 = AB + 3ED

Let AB = ED = h (as both are heights)

→ 150√3 = h + 3h

→ 150√3 = 4h

→ 37.5√3 = h

→ 64.95 = h

So, distance from first point = 64.95/√3 = 37.5 m

Another = 150 - 37.5 = 112.5 m

•°• Height of the pillar is 64.95 m and position of the point from the first point is 64.95/√3 m (37.5) and another is 112.5 m

$\rule{200}2$

Question:

In umbrella has 8 ribs which are equally spaced, as shown in the figure. Assuming the umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.

Solution:

There are total 8 ribs in the umbrella.

So,

Area of umbrella = 8 (Area of rib)

Area of rib = 1/8 (Area of umbrella)

→ 1/8 (Area of circle)

→ 1/8 × πr²

→ 1/8 × 22/7 × (45)²

→ 1/8 × 22/7 × 2025

→ 22275/28

→ 795.54 cm²

•°• Area between two consecutive ribs of umbrella is 795.54 cm²