Question

11.
image of a right triangle with one angle 60°, hypotenuse 3
find the length of the short leg.
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find the length of the long leg.
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Explanation:

Step1: Identify the triangle type

This is a 30 - 60 - 90 right - triangle. The side opposite the 30° angle is the short leg, the side opposite the 60° angle is the long leg, and the hypotenuse is opposite the 90° angle. In a 30 - 60 - 90 triangle, the hypotenuse \(c\) is twice the length of the short leg \(a\) (i.e., \(c = 2a\)), and the long leg \(b=\sqrt{3}a\). Here, the hypotenuse is given as 3.

Step2: Find the short leg

Using the formula \(c = 2a\), where \(c = 3\). We solve for \(a\):
\(a=\frac{c}{2}=\frac{3}{2} = 1.5\)

Step3: Find the long leg

Using the formula \(b=\sqrt{3}a\), and we know \(a = \frac{3}{2}\). So,
\(b=\sqrt{3}\times\frac{3}{2}=\frac{3\sqrt{3}}{2}\approx2.598\)

Answer:

Length of the short leg: \(\frac{3}{2}\) (or \(1.5\))
Length of the long leg: \(\frac{3\sqrt{3}}{2}\) (or approximately \(2.60\))