Question

Use the equation to find the length of the missing leg measure. NOTE: Type in numerical answers only to receive credit. (3 points) a2+162=202 1. Evaluate the powers: a2+ =400 2. Isolate the variable: a2= 3. Take the square root of both sides: a2−−√=144−−−√ 4. The missing side length is a= Skip to navigation

Answer 1

Let's solve the equation step by step.

1. Start with the given equation: \[ a^2 + 162 = 202 \]

2. Subtract 162 from both sides to isolate \( a^2 \): \[ a^2 = 202 - 162 \] \[ a^2 = 40 \]

3. Take the square root of both sides to solve for \( a \): \[ a = \sqrt{40} \]

4. Simplifying \( \sqrt{40} \): \[ \sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10} \]

Thus, the missing side length is: \[ a = 2\sqrt{10} \]

If you need a numerical approximation, \( \sqrt{10} \approx 3.162 \), so: \[ a \approx 2 \times 3.162 \approx 6.324 \]

However, if you are looking for an exact numerical answer to enter, you should enter: \[ 2\sqrt{10} \] or its approximate value: \[ 6.324 \] (Note: Please clarify if you need the exact form or the numerical approximation.)