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 $\csc \mathrm { B }$ when $\mathrm { a } = 6$ and $\mathrm { b } = 7$
A) $\frac { \sqrt { 85 } } { 7 }$
B) $\frac { 7 \sqrt { 85 } } { 85 }$
C) $\frac { \sqrt { 85 } } { 6 }$
D) $\frac { 6 \sqrt { 85 } } { 85 }$

Question

Quizplus · Accepted Answer

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we have:$$c^2 = a^2 + b^2$$Substituting the given values, we get:$$c^2 = 6^2 + 7^2 = 36 + 49 = 85$$Taking the square root of both sides, we get:$$c = \sqrt{85}$$The cosecant of an angle is defined as the ratio of the hypotenuse to the side opposite the angle. In this case, the angle B is opposite the side b, so we have:$$\csc B = \frac{c}{b} = \frac{\sqrt{85}}{7}$$Therefore, the correct answer is A.

Suppose ABC Is a Right Triangle with Sides of Lengths csc⁡B\csc \mathrm { B }cscB

Suppose ABC Is a Right Triangle with Sides of Lengths $\csc \mathrm { B }$