Question

In a right angle triangle, the base angle is 45', where as the side length is 3 dm, The length of perpendicular is:​

Answer 1

Given:

In a right-angled triangle, the base angle is 45', whereas the side length is 3 dm

To find:

The length of the perpendicular

Solution:

Assuming Δ ABC as the triangle right-angled at B

∠ACB = 45° = base angle

BC = 3 dm = side length

AB = the perpendicular

Now, according to the trigonometric ratios of a triangle, we have

$\boxed{\bold{tan\:\theta = \frac{Perpendicular}{Base} }}$

Here θ = 45°

∴ $tan\:45\° = \frac{AB}{BC}$

on substituting the given values, we get

$\implies 1 = \frac{AB}{3}$

$\implies \bold{ AB =3}$

Thus, the length of the perpendicular is → 3 dm.

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