Question 70.
A TV relay antenna is erected at the top of a hill with a slope of 40 degrees. From the base of the hill, the elevation of the top of the antenna is 50.4 degrees. At a point 300 m uphill, the elevation of the same top is 62.2 degrees. Find the height of the antenna from the base of the hill.
BC is the path leading to the top C of the hill on which there is a point E at 300 m from B.
Join ED.
m ∠ABC = 40°, m ∠ABD = 50.4° and
m ∠DEF = 62.2° (as given)
m ∠EBD = 10.4° and m ∠EDB = 11.8°
(as worked out from the given angles and
as shown in the figure)
Applying sine law to ΔEBD,
=> DE/sin10.4° = 300/sin11.8°
=> DE = 264.8 m
Height of antenna from the base of the hill, AD
= BEsin40° + DEsin62.2°
= 300sin40° + 264.8sin62.2°
= 192.8 + 234.2 m
= 427 m.
LINK to YA!
A TV relay antenna is erected at the top of a hill with a slope of 40 degrees. From the base of the hill, the elevation of the top of the antenna is 50.4 degrees. At a point 300 m uphill, the elevation of the same top is 62.2 degrees. Find the height of the antenna from the base of the hill.
Answer 70.
AB is the base of the hill. (Refer to the figure.)
AD is the height of antenna from base A of the hill.BC is the path leading to the top C of the hill on which there is a point E at 300 m from B.
Join ED.
m ∠ABC = 40°, m ∠ABD = 50.4° and
m ∠DEF = 62.2° (as given)
m ∠EBD = 10.4° and m ∠EDB = 11.8°
(as worked out from the given angles and
as shown in the figure)
Applying sine law to ΔEBD,
=> DE/sin10.4° = 300/sin11.8°
=> DE = 264.8 m
Height of antenna from the base of the hill, AD
= BEsin40° + DEsin62.2°
= 300sin40° + 264.8sin62.2°
= 192.8 + 234.2 m
= 427 m.
LINK to YA!
Thank you very much for helping me with this problem. It really helped me a lot. n_n
ReplyDeleteThank you Jason for the appreciation.
ReplyDelete