Question

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

Answer 1

Answer:

$a =22$

$b = 11$

Step-by-step explanation:

Given

See attachment for triangle

Required

Find a and b

Using cosine formula, we have:

$\cos \theta = \frac{Adjacent}{Hypotenuse}$

So, we have:

$\cos (30) = \frac{11\sqrt 3}{a}$

Make a the subject

$a = \frac{11\sqrt 3}{\cos (30)}$

$\cos(30) = \frac{\sqrt 3}{2}$

So, we have:

$a = \frac{11\sqrt 3}{\frac{\sqrt 3}{2}}$

Rewrite as:

$a = 11\sqrt 3 \div \frac{\sqrt 3}{2}$

This gives:

$a = 11\sqrt 3 * \frac{2}{\sqrt 3}$

$a = 11 * 2$

$a =22$

To solve for b, we use Pythagoras theorem

$a^2 = b^2 + (11\sqrt 3)^2$

$22^2 = b^2 + (11\sqrt 3)^2$

$484 = b^2 + 363$

Collect like terms

$b^2 = 484 - 363$

$b^2 = 121$

Take positive square roots

$b = \sqrt {121$

$b = 11$