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Find the missing side lengths.Leave your answers as radicals in simplest form.

Find the missing side lengths.Leave your answers as radicals in simplest form.-example-1

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Answer:

a = 4

b = 4

Explanation:

NOTE: THIS EXPLANATION ASSUMES YOU HAVE A BASIC UNDERSTANDING OF COMMON TRIANGLES, PYTHAGOREAN THEOREM, ISOCELES TRIANGLE THEOREM, AND BASIC ALGEBRA

Since the triangle is a right triangle, and you know one of the angles is a 45 degree angle, you know the other angle is a 45 degree angle. This is a classic 45-45-90 right triangle.

If two angles are equal two each other the opposite sides of the corresponding angles are also equal each other, courtesy of the isosceles triangle theorem.

So if a = b, we can just substitute one for the other. For this explanation, I'll be using 'a' for both 'a' and 'b'.

The Pythagorean Theorem is

a^2 + b^2 = c^2

Since a = b we can say

a^2 + a^2 = c^2

Then simplify

2a^2 = c^2

Now let's just substitute the numbers

2a^2 = (4
√(2))^2

2a^2 = 32

a^2 = 16

a = 4

Since 'a' and 'b' are equal, 'b' also equals 4.

Hope this helped! :)

User Sarunw
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