Chapter 9.7, Problem 22E

To determine

Tofind:The value of $x$

Explanation of Solution

Given information:

  ${45}^{\circ }-{45}^{\circ }-{90}^{\circ }$ triangle

Concept Used:

In a right-angled triangle ABC, tangent for acute angle $\angle A$ is the ratio of length of side opposite to angle $\angle A$ to the length of side adjacent to $\angle A$

We know,in a ${45}^{\circ }-{45}^{\circ }-{90}^{\circ }$ right angled triangle, length of both legs are equal.

Therefore $\tan A$ for both the angles will always be-

  $\tan A=\frac{a}{a}=1$

Or we can say in both cases it will be-

  $\tan {45}^{\circ }=1$