Question

in triangle abc angle abc is equals to 90 degree and Angle ACB is equal to 30 degrees and ac is equals to 10 cm find the length of AB​

Answer 1

The length of AB​ of triangle ABC is 5 cm.

Step-by-step explanation:

It is given that,

In Δ ABC,

∠ABC = 90°

∠ACB = 30°

AC = 10 cm

Referring to the figure attached below and using the right-angled triangle trigonometry properties, we get

AB = Perpendicular

BC = Base

AC = Hypotenuse

Now,

sin θ = $\frac{Perpendicular}{Base} = \frac{AB}{AC}$

here θ = 30°

∴ sin 30° = $\frac{AB}{10}$

⇒ $\frac{1}{2} = \frac{AB}{10}$

⇒ AB = $\frac{10}{2}$

⇒ AB = 5 cm

Thus, the length of AB is 5 cm.

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