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.
the length of the missing side of the right triangle is a =

Explanation:

Step1: Recall Pythagorean Theorem

For a right triangle with legs \(a\), \(b\) and hypotenuse \(c\), the Pythagorean Theorem is \(a^{2}+b^{2}=c^{2}\). We know \(b = 8\) and \(c=10\), and we need to find \(a\). Rearranging the formula to solve for \(a\), we get \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute values into the formula

Substitute \(c = 10\) and \(b=8\) into the formula: \(a=\sqrt{10^{2}-8^{2}}=\sqrt{100 - 64}=\sqrt{36}\).

Step3: Simplify the square root

\(\sqrt{36}=6\), so \(a = 6\).

Answer:

6