Question

$\huge{\tt{\underline{Help!!}}}$
❄️An arch is in the form of a semi- ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.❄️
Ans:- 1.56 m ​

Answer 1

QUESTION :-

An arch is in the form of a semi- ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.

ANSWER:-

Let us take a point B on x - axis.

Such that AB = 1.5 m

AC⊥0B

∴ 0A = 4-1.5

= 2.5 m

∴ The x - coordinates of point C is 2.5 .

Substituting the value of x with 2.5 in the equation of semi ellipse we get,

$( \frac{(2.5){}^{2} }{16} ) - \frac{y {}^{2} }{4} = 1 \\ (i.e) \frac{y {}^{2} }{4} = 1 - \frac{6.25}{16} \\.°. y {}^{2} = 4( \frac{6.25 - 16}{6.25} ) \\ .°.y {}^{2} = 4( \frac{9.75}{6.25} ) \\ .°.y {}^{2} = 2.4375 \\ y = \sqrt{2.4375} \\ .°.y = 1.56 \: (approx) \\ .°. \: ac = 1.56m.$

Thus ,

the length of the arc at a point 1.5 m from one end is approximately 1.56 m

THANKS.

Answer 2

Explanation:

have a bright future ahead....

thanks....