actors at P and R have to stand 5m and 4m away from the actor at Q respectively. The angle of elevation of S from P is 45° and the angle of elevation of S from R is 60°. If the spotlight is placed at a point vertically above PR. 60 R Pe 5m 4m a) Determine how far the actors at P and R must stand from 105 each other.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter3: Triangles
Section3.5: Inequalities In A Triangles
Problem 23E: An auto parts dealer in Huntsville, Alabama at point H, has called a manufacturer for parts needed...
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Q :
actors at P and R have to stand 5m and 4m away from the
actor at Q respectively. The angle of elevation of S from P
is 45° and the angle of elevation of S from R is 60°. If the
spotlight is placed at a point vertically above PR.
60°
R
P
5m
4m
a) Determine how far the actors at P and R must stand from
105
each other.
b) The actor at P makes his entrance on stage by sliding
down a wire from S to P. How long is the wire that the
actor slides along?
In the diagram alongside, D is a point vertically above C.
DC is y meters in length. The angle of elevation of D from
B is 8. Angle DÂB = a and DBA = B.
a) Determine the length of DB in terms y and 8.
ysin (a+ B)
b) Show that AB =
135
sin e sin a
In the diagram alongside, C is a point vertically above D.
CD is y meters in length. The angle of elevation of C from
B is O and the angle of elevation of C from A is a. Angle
ADB = B.
a) Determine the length of AD in terms y and a.
b) Determine the length of BD in terms y and 6.
y? sin B
c) Hence, show that the area of AABD =
A
B
2 tan a tan 0
Copyright Kevin Smith / Berlut Books CC
128
7) A telephone cable is to be erected between 2 cliff sides AD
and BE. An engine
horizontal plane as the foot of the cliffs. He measures the
angle of E from C and D to be 0 and a respectively. Cliff
DA is y meters in height and C is x meters from the foot
stands
point C in the same
D
y
of cliff BE.
a) Show that the length of the telephone cable is
x tan 8- y
sin a
b) If x=1000m, y = 250m and 0 = a = 45°, what is the
distance between the cliffs?
Mixed Exercise: (answers on page 352)
Transcribed Image Text:= D Maths_Hadbook... E Q : actors at P and R have to stand 5m and 4m away from the actor at Q respectively. The angle of elevation of S from P is 45° and the angle of elevation of S from R is 60°. If the spotlight is placed at a point vertically above PR. 60° R P 5m 4m a) Determine how far the actors at P and R must stand from 105 each other. b) The actor at P makes his entrance on stage by sliding down a wire from S to P. How long is the wire that the actor slides along? In the diagram alongside, D is a point vertically above C. DC is y meters in length. The angle of elevation of D from B is 8. Angle DÂB = a and DBA = B. a) Determine the length of DB in terms y and 8. ysin (a+ B) b) Show that AB = 135 sin e sin a In the diagram alongside, C is a point vertically above D. CD is y meters in length. The angle of elevation of C from B is O and the angle of elevation of C from A is a. Angle ADB = B. a) Determine the length of AD in terms y and a. b) Determine the length of BD in terms y and 6. y? sin B c) Hence, show that the area of AABD = A B 2 tan a tan 0 Copyright Kevin Smith / Berlut Books CC 128 7) A telephone cable is to be erected between 2 cliff sides AD and BE. An engine horizontal plane as the foot of the cliffs. He measures the angle of E from C and D to be 0 and a respectively. Cliff DA is y meters in height and C is x meters from the foot stands point C in the same D y of cliff BE. a) Show that the length of the telephone cable is x tan 8- y sin a b) If x=1000m, y = 250m and 0 = a = 45°, what is the distance between the cliffs? Mixed Exercise: (answers on page 352)
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