In the figure below AB and CD are perpendicular to BC and the size of angle ACB is 31°. Find the length of segment BD.

Answers
Answer:
Use right triangle ASCITES: tan(31o) = 6 / BC , solve: BC = 6 / tan(31o)
Use Pythagora's theorem in the right angled triangle...
The length of the segment BD = 11.870
Given:
In a figure AB and CD are perpendicular to BC
The measurement of angle ACB is 31°
To find:
The length of segment BD.
Solution:
Given AB and CD are perpendicular to BC
From figure AB = 6 and CD = 9
From figure, ABC is right angled triangle
[ the figure is attached below ]
Here, AB = 6 and ∠ACB = 31°
As we know in right angle triangle tan θ = oppo side/adj side
⇒ tan 31° = AB/BC
⇒ BC = 6/tan 31
Now consider BCD is also a right angled triangle
From Pythagorean theorem
⇒ BD² = BC² + CD²
⇒ BD² = (6/tan 31)² + 9²
⇒ BD² = (36/0.6008) + 81 [∵ since tan 31° = 0.6008 ]
⇒ BD² = 59.92 + 81
⇒ BD² = 140.920
⇒ BD = 11.870 (approx)
The length of the segment BD = 11.870
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