Chapter 5, Problem 93A

(a)

To determine

To identify: The longer side of the triangle for the given specification.

Answer to Problem 93A

Side A is longer than B .

Explanation of Solution

Given:

Two sides of a right-angled triangle are A and B .

  $\tan \theta =\frac{A}{B}$

  $\tan \theta >1$

Calculation:

It is given that $\tan \theta =\frac{A}{B}$ and $tan\theta >1$

For the given condition, $tan\theta >1$

  $\begin{array}{l}\frac{A}{B}>1\\ A>B\end{array}$

Conclusion:

Therefore, side A is longer than side B .

(b)

To determine

To identify: The longer side of the triangle for the given specification.

Answer to Problem 93A

Side B is longer than A

Explanation of Solution

Given:

Two sides of a right-angled triangle are A and B .

  $\tan \theta =\frac{A}{B}$

  $\tan \theta <1$

Calculation:

It is given that $\tan \theta =\frac{A}{B}$ and $tan\theta <1$

For the given condition, $tan\theta <1$

  $\begin{array}{l}\frac{A}{B}<1\\ A<B\end{array}$

Conclusion:

Therefore, side B is longer than side A .

(c)

To determine

To explain: The meaning of the given condition.

Answer to Problem 93A

For the given condition, both sides A and B are equal and $\theta =45°$ .

Explanation of Solution

Given:

Two sides of a right-angled triangle are A and B .

  $\tan \theta =\frac{A}{B}$

  $\tan \theta =1$

Calculation:

It is given that $\tan \theta =\frac{A}{B}$ and $tan\theta =1$

For the given condition, $tan\theta =1$

  $\begin{array}{l}\frac{A}{B}=1\\ A=B\end{array}$

Also,

  $\begin{array}{l}\tan \theta =1\\ \theta ={\tan }^{-1}\left(1\right)\\ \theta =45°\end{array}$

Conclusion:

Therefore, for the given condition, side A and B are equal in length.