Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given
angle. Give exact answers with rational denominators.
-Find $\tan B$ when $a = 4$ and $b = 5$.
A) $\frac { 5 \sqrt { 41 } } { 41 }$

B) $\frac { 4 \sqrt { 41 } } { 41 }$

C) $\frac { 4 } { 5 }$

D) $\frac { 5 } { 4 }$

Question

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given
angle. Give exact answers with rational denominators.
-Find $\tan B$ when $a = 4$ and $b = 5$.
A) $\frac { 5 \sqrt { 41 } } { 41 }$

B) $\frac { 4 \sqrt { 41 } } { 41 }$

C) $\frac { 4 } { 5 }$

D) $\frac { 5 } { 4 }$

Quizplus · Accepted Answer

In a right triangle, $\tan B = \frac{opposite}{adjacent}$, so $\tan B = \frac{a}{b} = \frac{4}{5}$. However, since $a = 4$ and $b = 5$ are given for sides opposite and adjacent to angle B respectively, the correct calculation should be $\tan B = \frac{b}{a} = \frac{5}{4}$, making option D correct.

Two Sides of a Right Triangle ABC (C Is the Right