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 sec $B$ when $a = 9$ and $b = 5$.
A) $\frac { 9 \sqrt { 106 } } { 106 }$

B) $\frac { \sqrt { 106 } } { 9 }$

C) $\frac { 9 \sqrt { 106 } } { 5 }$

D) $\frac { 5 \sqrt { 106 } } { 106 }$

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 sec $B$ when $a = 9$ and $b = 5$.
A) $\frac { 9 \sqrt { 106 } } { 106 }$

B) $\frac { \sqrt { 106 } } { 9 }$

C) $\frac { 9 \sqrt { 106 } } { 5 }$

D) $\frac { 5 \sqrt { 106 } } { 106 }$

Quizplus · Accepted Answer

To find sec(B), we need the hypotenuse, which is $\sqrt{a^2 + b^2} = \sqrt{9^2 + 5^2} = \sqrt{81 + 25} = \sqrt{106}$. Sec(B) is the reciprocal of cos(B), which is adjacent/hypotenuse = 9/$\sqrt{106}$. Rationalizing gives $\frac{\sqrt{106}}{9}$.

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