Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th
Advertisement Remove all ads

A statue 1.6 m tall stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60ϒ and from the same point the angle of elevation of the top of th - Mathematics

Sum

A statue 1.6 m tall stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60ϒ and from the same point the angle of elevation of the top of the pedestal is 40ϒ. Find the height of the pedestal. (tan 40° = 0.8391, `sqrt(3)` = 1.732)

Advertisement Remove all ads

Solution

Height of the statue = 1.6 m

Let the height of the pedestal be “h”

AD = H + 1.6 m

Let AB be x

In the right ∆ABD, tan 60° = `"AD"/"AB"`

`sqrt(3) = ("h" + 1.6)/x`

x = `("h" + 1.6)/sqrt(3)`  ...(1)


In the right ∆ABC, tan 40° = `"AC"/"AB"`

0.8391 = `"h"/x`

x = `"h"/(0.8391)`

Substitute the value of x in (1)

`"h"/(0.8391) = ("h" + 1.6)/sqrt(3)`

(h + 1.6) 0.8391 = `sqrt(3)` h

0.8391 h + 1.34 = 1.732 h

1.34 = 1.732 h – 0.8391 h

1.34 = 0.89 h

h = `1.34/0.89`

= `134/89`

= 1.5 m

Height of the pedestal = 1.5 m

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Samacheer Kalvi Mathematics Class 10 SSLC Tamil Nadu State Board
Chapter 6 Trigonometry
Exercise 6.2 | Q 4 | Page 257
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×