Chapter 9.7, Problem 9E

To determine

Tofind:Tangent of each acute angle

Answer to Problem 9E

  $\tan A=\frac{24}{7}$

  $\tan B=\frac{7}{24}$

Explanation of Solution

Given information:

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 $\angle A$

Calculation:

The two acute angles are $\angle A$ and $\angle B$

Basis definition we can say-

  $\begin{array}{l}\tan A=\frac{opposite}{adjacent}\\ \Rightarrow \tan A=\frac{BC}{AC}\\ \Rightarrow \tan A=\frac{72}{21}\\ \Rightarrow \tan A=\frac{24}{7}\end{array}$

  $\begin{array}{l}\tan B=\frac{opposite}{adjacent}\\ \Rightarrow \tan B=\frac{AC}{BC}\\ \Rightarrow \tan B=\frac{21}{72}\\ \Rightarrow \tan B=\frac{7}{24}\end{array}$