Math, asked by BabyMin, 6 days ago

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

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Answers

Answered by flanker
1

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 (\sqrt{x} 3-1)

The -1 is brought from tan 30 as cot 30 is its opposite.

Hope it helps

Answered by amitnrw
7

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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