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6 problems match “special right triangles”. Clear

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1. Third side of a 30-60-90 triangle ●○○○○ 10 ptsA right triangle has two interior angles of $30^\circ$ and $90^\circ$, and two of its side lengths are $5$ and $5\sqrt{3}$. Find the third side length.
2. Sum of legs in a 30-60-90 triangle ●○○○○ 10 ptsA 30-60-90 right triangle has hypotenuse $2\sqrt{6}$ centimeters. Find the sum of the lengths, in centimeters, of its two legs. Round to two decimal places.
3. Altitude of an equilateral triangle ●○○○○ 10 ptsAn equilateral triangle has side length 6 cm. Find the length of its altitude. Round to two decimal places.
4. Sides of a 30-60-90 triangle ●○○○○ 10 ptsTriangle $ABC$ has angles $30^\circ$, $60^\circ$ and $90^\circ$, and its shortest side has length $3$ units. Find the lengths of the other two sides, in increasing order. Round to two decimal places.
5. Cubed sine at half angle ●○○○○ 10 ptsIf $\theta = 60^\circ$, find the value of $4\sin^3\frac{\theta}{2}$. Give your answer as a decimal.
6. Area of a 30-60-90 triangle ●●○○○ 20 ptsA right triangle has angles of $30^\circ$ and $60^\circ$. The altitude from the right-angle vertex to the hypotenuse is $3$ units. Find the area of the triangle in square units. Round your answer to two decimal places.