In the figure below, what is the length of AB?
A. 45√3 m
B.(45/√3)m
C. 45 (√3 - 1) m
D. 45 (√3 + 1) m
Answers
Answer: C. 45 (√3 - 1) m
Step-by-step explanation:
45m of perpendicular is given.
Since 30 degrees is the angle at the edge we will take that and use cot 30 to derive 45 ()
The -1 is brought from tan 30 as cot 30 is its opposite.
Hope it helps
The length of AB in given figure is 45 (√3 - 1) m
tan θ
"The tangent of an acute angle (θ) in a right triangle is the ratio of the side opposite of the angle to the side adjacent to the angle"
Step 1:
In Right angle ΔBCD
tan 45° = DC/BC
Step 2:
Substitute DC = 45 m and tan 45° = 1 and solve for length of BC
1 = 45/BC
=> BC = 45 m
Step 3:
In Right angle ΔACD
tan 35° = DC/AC
Step 4:
Substitute DC = 45 m and tan 30° = 1/√3 and solve for length of AC
1/√3 = 45/AC
=> AC = 45√3 m
Step 5:
Subtract BC from AC to get AB using Segment Addition postulate
AB = AC - BC
AC = 45√3 - 45
AC = 45(√3 - 1) m
Correct option is C) 45 (√3 - 1) m
The length of AB in given figure is 45 (√3 - 1) m
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