Question

^Applications of trigonometry
question is in the attachment
^^please show the working as well thankyou so much​

Answer 1

Step by step calculation :- 1

↝ Let AB be the pillar and the peacock is sitting at the top A of the pillar.

↝ Therefore, AB = 9 meter.

↝ Let the hole be at B.

↝ Let assume that the snake is at C when the peacock notices the snake such that BC = 27 m

↝ Let assume that  v m/sec be the speed of both the snake.

↝ Let the peacock catches the snake after t seconds at point D.

As speed of the snake and peacock is same,

↝ Therefore, distance travelled by the snake in t seconds is same as the distance travelled by peacock.

↝ Let snake caught at point D which is at a distance of 'x' meters from the hole B.

↝ Therefore, BD = 'x' meter.

↝ Now, BC = 27 meter,

↝ Therefore, AC = CD = BC - BD = (27 - x) meter.

Now,

↝ In ∆ ABD

↝ By pythagoras theorem,

⇛ AD² = AB² + BD²

On substituting the values od AD, AB and BD, we get

$\rm :\longmapsto\: {(27 - x)}^{2} = {x}^{2} + {(9)}^{2}$

$\rm :\longmapsto\: {(27)}^{2} + \cancel{{x}^{2}} - 54x = \cancel{{x}^{2}}+81$

$\rm :\longmapsto\:729 - 54x = 81$

$\rm :\longmapsto\: - 54x = 81 - 729$

$\rm :\longmapsto\: - 54x = - 648$

$\bf\implies \:x = 12$

↝ Hence, the snake is caught at a distance of 12m from the hole.

Additional Information :-

Writing System of Equation from Word Problem.

↝ 1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

↝ 2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

↝ 3. Carry out the plan and solve the problem.