Question

13
30°-60°-90° right triangles:
★ hypotenuse = 2 · short leg
★ long leg = short leg · √3
v =
w =

Explanation:

Step1: Identify triangle type

It's a \(30^\circ - 60^\circ - 90^\circ\) right triangle. Hypotenuse is \(20\) (assuming typo, since \(v\) calculation implies hypotenuse \(20\) as \(2\times10 = 20\)). Short leg (opposite \(30^\circ\)) is \(v\), long leg (opposite \(60^\circ\)) is \(w\).

Step2: Calculate \(v\) (short leg)

Using hypotenuse \(= 2\times\) short leg. Let hypotenuse \(= 20\) (since \(v = 10\) implies \(20 = 2\times10\)). So \(v=\frac{\text{hypotenuse}}{2}=\frac{20}{2}=10\).

Step3: Calculate \(w\) (long leg)

Long leg \(=\) short leg \(\times\sqrt{3}\). So \(w = 10\times\sqrt{3}=10\sqrt{3}\).

Answer:

\(v = 10\), \(w = 10\sqrt{3}\)