The angles of elevation of the top of a tower from two points at a distance of 4 m and
9 m from the base of the tower and in the same straight line with it are complementary.
Prove that the height of the tower is 6 m.
Answers
Answered by
1
Answer:
not proved as the are not provable through the pythogoras theorm
Answered by
9
Answer:
⇨★ Let AB be the tower. C and D be the two points with distance 4 m and 9 m from the base respectively. As per question,
In right ΔABC,
tan x = AB/BC
tan x = AB/4
AB = 4 tan x … (i)
Again, from right ΔABD,
tan (90°-x) = AB/BD
cot x = AB/9
AB = 9 cot x … (ii)
Multiplying equation (i) and (ii)
AB2 = 9 cot x × 4 tan x
⇒ AB2 = 36 (because cot x = 1/tan x
⇒ AB = ± 6
Since height cannot be negative. Therefore, the height of the tower is 6 m.
Hence Proved.
_____________________________________
Attachments:
Similar questions
Math,
5 months ago
Math,
5 months ago
Math,
11 months ago
Social Sciences,
1 year ago
Math,
1 year ago