Question

use the pythagorean theorem to find the length of the missing side of the right triangle. then find the value of each of the six trigonometric functions of θ. complete the table by using the names of the sides to express each trigonometric function as a ratio. sin θ = bc/ab, csc θ = ab/bc, cos θ = ac/ab, sec θ = ab/ac, tan θ = bc/ac, cot θ = ac/bc. the length of the missing side of the right triangle is . (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall Pythagorean Theorem

The Pythagorean Theorem for a right - triangle is \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs of the right - triangle. Here, \(a = 6\) and \(b = 8\).

Step2: Calculate the hypotenuse

Let \(AB\) be the hypotenuse. Then \(AB=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}=10\).

Answer:

10