The diagram below shows the cross-section ABCD of a gutter made using a sheet of metal 25cm wide. The sheet of metal is bent such that AB and CD are both 5cm long and inclined to BC at an angle 0 radians. 5 cm 5 cm E h cm 15 (i) Show that the area of the cross-section of the gutter, S cm², is given by S = 25 sin 0 (3+cos0). Find the maximum possible cross-sectional area that can be constructed, showing clearly how you obtain the value. (ii) Water fills the gutter in such a way, that at timet seconds, the depth of water is h cm and EBCF represents the cross-section of the portion of the gutter filled with water as shown in the diagram. Given that 0 find an expression for the angle FBC in terms of h. 4 When the depth of water in the gutter is 1.5 cm, the water level is rising at a rate of 0.4 cm s-l. Find the rate at which angle FBC is increasing at this instant. [(i) 78.7 cm? (ii) ZFBC = tan h 0.0219 rads] 15+h)
The diagram below shows the cross-section ABCD of a gutter made using a sheet of metal 25cm wide. The sheet of metal is bent such that AB and CD are both 5cm long and inclined to BC at an angle 0 radians. 5 cm 5 cm E h cm 15 (i) Show that the area of the cross-section of the gutter, S cm², is given by S = 25 sin 0 (3+cos0). Find the maximum possible cross-sectional area that can be constructed, showing clearly how you obtain the value. (ii) Water fills the gutter in such a way, that at timet seconds, the depth of water is h cm and EBCF represents the cross-section of the portion of the gutter filled with water as shown in the diagram. Given that 0 find an expression for the angle FBC in terms of h. 4 When the depth of water in the gutter is 1.5 cm, the water level is rising at a rate of 0.4 cm s-l. Find the rate at which angle FBC is increasing at this instant. [(i) 78.7 cm? (ii) ZFBC = tan h 0.0219 rads] 15+h)
Trigonometry (MindTap Course List)
10th Edition
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Chapter2: Analytic Trigonometry
Section2.1: Using Fundamental Identities
Problem 67E
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Full solution for part ii. Thank you. Solution can be found below the qn
![The diagram below shows the cross-section ABCD of a gutter made using a sheet of metal
25cm wide. The sheet of metal is bent such that AB and CD are both 5cm long and inclined
to BC at an angle 0 radians.
A
5 cm
5 сту
E
h cm
15
(i)
Show that the area of the cross-section of the gutter, S cm², is given by
S = 25 sin 0(3+cos 0).
Find the maximum possible cross-sectional area that can be constructed, showing
clearly how you obtain the value.
(ii) Water fills the gutter in such a way, that at timet seconds, the depth of water is
h cm and EBCF represents the cross-section of the portion of the gutter filled with
water as shown in the diagram.
Given that 0
find an expression for the angle FBC in terms of h.
4
When the depth of water in the gutter is 1.5 cm, the water level is rising at a rate of 0.4
cm s-l. Find the rate at which angle FBC is increasing at this instant.
[(i) 78.7 cm?
h
; 0.0219 rads]
(ii) ZFBC = tan
-1
15+h](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F028ae6fb-3e0a-41c8-b701-7e8359e99365%2Fc05c3d31-6517-495c-8bd1-e709c40ea655%2Fhrjflri_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The diagram below shows the cross-section ABCD of a gutter made using a sheet of metal
25cm wide. The sheet of metal is bent such that AB and CD are both 5cm long and inclined
to BC at an angle 0 radians.
A
5 cm
5 сту
E
h cm
15
(i)
Show that the area of the cross-section of the gutter, S cm², is given by
S = 25 sin 0(3+cos 0).
Find the maximum possible cross-sectional area that can be constructed, showing
clearly how you obtain the value.
(ii) Water fills the gutter in such a way, that at timet seconds, the depth of water is
h cm and EBCF represents the cross-section of the portion of the gutter filled with
water as shown in the diagram.
Given that 0
find an expression for the angle FBC in terms of h.
4
When the depth of water in the gutter is 1.5 cm, the water level is rising at a rate of 0.4
cm s-l. Find the rate at which angle FBC is increasing at this instant.
[(i) 78.7 cm?
h
; 0.0219 rads]
(ii) ZFBC = tan
-1
15+h
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