Question

In a school assembly there are as many number of students in a row as the number of rows. If there are 1296 students in assembly,find number of students standing in row

Answer 1

Answer:

Find the area of the right angled triangle with hypothenuse 5 cm and one of the acute angle is 48°30'.

\purple{\large{\underline{\underline{ \rm{Solution: }}}}}

Solution:

Here, first we need to find AB and then BC. Therefore, by finding both height and breadth, we will apply the formula of area of right triangle.

From the figure,

For finding AB i.e, height (perpendicular)

\sf{ \sin C = \dfrac{perpendicular}{hypotenuse}}sinC=

hypotenuse

perpendicular

\sf \sin C = \dfrac{AB}{AC}sinC=

AC

AB

\sf{ \sin48 \degree30' = \dfrac{AB}{5}}sin48°30

′

=

5

AB

N.B :-

sin 48° = 0.7431

But we have sin 48°30'

Let's convert 30' into degrees, we have:

30' = 0.5°

Now 48° + 0.5° = 48.5°

∴ sin 48.5° = 0.7490

Let's continue.......

\sf{0.7490 = \dfrac{AB}{5}}0.7490=

5

AB

\sf5 \times 0.7490 = AB5×0.7490=AB5×0.7490=AB5×0.7490=AB

★\sf{AB = 3.7450 \: cm}AB=3.7450cm

For finding BC i.e, base

\sf \cos C = \dfrac{base}{hypotenuse}cosC=

hypotenuse

base

\sf{ \cos C = \dfrac{BC}{AC} }cosC=

AC

Answer 2

The number of students standing in row = 36

Given :

• In a school assembly there are as many number of students in a row as the number of rows.

• There are 1296 students in assembly

To find :

The number of students standing in row

Solution :

Step 1 of 2 :

Form the equation

Let number of students standing in row = N

Since there are as many number of students in a row as the number of rows

Then number of rows = N

Total number of students

= N × N

= N²

By the given condition

N² = 1296

Step 2 of 2 :

Find number of students standing in row

$\displaystyle \sf{ {N}^{2} = 1296 }$

$\displaystyle \sf \implies { {N}^{} = \sqrt{1296} }$

$\displaystyle \sf \implies { {N}^{} = 36 }$

Hence number of students standing in row = 36