Question

1. find the unknown side of the triangle below. 19.4 units 4 units 20.6 units 5 units

Explanation:

Step1: Identify triangle type

The triangle is right - angled (since there is a right - angle symbol at \(R\)). So we can use the Pythagorean theorem, which states that for a right - triangle with hypotenuse \(c\) and legs \(a\) and \(b\), \(c^{2}=a^{2}+b^{2}\). Here, the hypotenuse \(c = 20\) units and one leg \(a = 5\) units, and the other leg is \(x\) (the unknown side we need to find). We can re - arrange the Pythagorean theorem to solve for \(x\): \(x=\sqrt{c^{2}-a^{2}}\)

Step2: Substitute values into the formula

Substitute \(c = 20\) and \(a = 5\) into the formula \(x=\sqrt{c^{2}-a^{2}}\). First, calculate \(c^{2}-a^{2}\):
\(c^{2}-a^{2}=20^{2}-5^{2}=400 - 25=375\)

Step3: Calculate the square root

Now, find the square root of \(375\):
\(x=\sqrt{375}\approx19.3649\approx19.4\)

Answer:

19.4 units