Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th

# 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

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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)

#### 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?

#### APPEARS IN

Samacheer Kalvi Mathematics Class 10 SSLC Tamil Nadu State Board
Chapter 6 Trigonometry
Exercise 6.2 | Q 4 | Page 257