Question

If \[\tan x^{\circ}=\frac{5}{2}\], the length of CB is ______.

Options

• 0.4 m

• 40 m

• 50 m

• 80 m

Answer 1

If \[\tan x^{\circ}=\frac{5}{2}\], the length of CB is 40 m.

Explanation:

We know that,

\[\tan \theta = \frac{\text{Perpendicular}}{\text{Base}}\]

From figure,

In \[\triangle ABC,\]

\[\Rightarrow \tan x^\circ = \frac{AB}{CB}\]

\[\Rightarrow \frac{5}{2} = \frac{100}{CB}\]

\[\Rightarrow CB = \frac{2 \times 100}{5} = \frac{200}{5} = 40\ \text{m}.\]