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

Sep by step explanation pls​

Answer:

[tex]a =22[/tex]

[tex]b = 11[/tex]

Step-by-step explanation:

Given

See attachment for triangle

Required

Find a and b

Using cosine formula, we have:

[tex]\cos \theta = \frac{Adjacent}{Hypotenuse}[/tex]

So, we have:

[tex]\cos (30) = \frac{11\sqrt 3}{a}[/tex]

Make a the subject

[tex]a = \frac{11\sqrt 3}{\cos (30)}[/tex]

[tex]\cos(30) = \frac{\sqrt 3}{2}[/tex]

So, we have:

[tex]a = \frac{11\sqrt 3}{\frac{\sqrt 3}{2}}[/tex]

Rewrite as:

[tex]a = 11\sqrt 3 \div \frac{\sqrt 3}{2}[/tex]

This gives:

[tex]a = 11\sqrt 3 * \frac{2}{\sqrt 3}[/tex]

[tex]a = 11 * 2[/tex]

[tex]a =22[/tex]

To solve for b, we use Pythagoras theorem

[tex]a^2 = b^2 + (11\sqrt 3)^2[/tex]

[tex]22^2 = b^2 + (11\sqrt 3)^2[/tex]

[tex]484 = b^2 + 363[/tex]

Collect like terms

[tex]b^2 = 484 - 363[/tex]

[tex]b^2 = 121[/tex]

Take positive square roots

[tex]b = \sqrt {121[/tex]

[tex]b = 11[/tex]

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