In a 30-60-90 triangle, the hypotenuse is the shorter leg times the square root of two.

1 answer:

7 0

The correct answer is C "never."

The hypotenuse in a 30-60-90 triangle is the shorter leg doubled. So, it's 2x where x is the shorter leg.

In fact, the square root of two is not used to calculate any other sides in a 30-60-90 triangle. The shorter leg is x, the medium leg is x√3, and the hypotenuse is 2x.

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Given the question in the image, the following are the solution steps to answer the question

STEP 1: Write the general equation of an ellipse

$\frac{\mleft(x-h\mright)^2}{a^2}+\frac{(y-h)^2}{b^2^{}}=1$

STEP 2: Identify the parameters

the length of the major axis is 2a

the length of the minor axis is 2b

$\begin{gathered} 2a=24,a=\frac{24}{2}=12 \\ 2b=20,b=\frac{20}{2}=10 \end{gathered}$

STEP 3: Get the equation of the ellipse

$\begin{gathered} By\text{ substitution,} \\ \frac{(x-h)^2}{a^2}+\frac{(y-h)^2}{b^2}=1 \\ \frac{(x-0)^2}{12^2}+\frac{(y-0)^2}{10^2}=1=\frac{x^2}{144}+\frac{y^2}{100}=1 \end{gathered}$

STEP 4: Pick the nearest equation from the options,

Hence, the equation of the ellipse in the image is given as: