Given the triangle below, determine the missing side(s) without using the Pythagorean theorem (make sure your answer is fully simplified).

Which of the following sets of side lengths could represent the side lengths of a $30$-$60$-$90$ triangle?

Give the exact value of each expression. See Example 5. cos 30°

Without using a calculator, determine all values of P in the interval $\(\left\)[0\(\degree\),90\(\degree\]\right\))$ with the following trigonometric function value.

$\(\csc\) P=\(\sqrt\)2$

Given the triangle below, determine the missing side(s) without using the Pythagorean theorem (make sure your answer is fully simplified).

Without using a calculator, determine all values of A in the interval $\(\left\)[0,\(\frac{\pi}{2}\]\right\))$ with the following trigonometric function value.

$\(\cos\) A=\(\frac{\sqrt3}{2}\)$

Use the given triangles to evaluate each expression. If necessary, express the value without a square root in the denominator by rationalizing the denominator.

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