Chapter 8.4, Problem 54PPS

To determine

The tangent of the greater acute angle.

Answer to Problem 54PPS

  $\begin{array}{l}\tan 48°=\frac{\text{4}}{\text{3}}\\ \tan 48°=\text{1}\text{.33}\end{array}$

Explanation of Solution

Given:

The side lengths are 3, 4 and 5 centimeters.

Calculation:

The lengths form a Pythagorean triple; hence, the triangle is a right triangle. The greater acute angle is opposite to the greater leg.

Let x is the greater acute angle. The figure can be drawn as:

According to the definition of the Tangent function,

  $\begin{array}{l}\tan x°=\frac{\text{Opp}\text{.}}{\text{Adj}\text{.}}\\ \tan x°=\frac{\text{4}}{\text{3}}\\ \tan x°=\text{1}\text{.33}\end{array}$