Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using
the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize
the denominator if applicable.
-Find $\tan B$ when $b = 8$ and $c = 9$.
A) $\frac { \sqrt { 17 } } { 9 }$
B) $\frac { 8 \sqrt { 17 } } { 17 }$
C) $\frac { 9 \sqrt { 17 } } { 17 }$
D) $\frac { \sqrt { 17 } } { 8 }$

Question

Quizplus · Accepted Answer

First, use the Pythagorean theorem $a^2 + b^2 = c^2$ to find $a$. Given $b = 8$ and $c = 9$, we have $a^2 + 8^2 = 9^2$, which simplifies to $a^2 + 64 = 81$. Solving for $a$ gives $a^2 = 17$, so $a = \sqrt{17}$. Then, $\tan B = \frac{opposite}{adjacent} = \frac{a}{b} = \frac{\sqrt{17}}{8}$. However, since $\tan B$ is actually $\frac{opposite}{adjacent}$ from the perspective of angle B, and the opposite side is $b = 8$ and the adjacent side is $a = \sqrt{17}$, the correct expression for $\tan B$ is $\frac{8}{\sqrt{17}}$, which, when rationalized, is $\frac{8\sqrt{17}}{17}$.

Suppose ABC Is a Right Triangle with Sides of Lengths tan⁡B\tan BtanB

Suppose ABC Is a Right Triangle with Sides of Lengths $\tan B$