
A vertical pole of length 6m casts a shadow 4m long on the ground and at the same time a tower casts a shadow 28m long. Find the height of the tower.

Answer
500.7k+ views
Hint:We will be using the concepts of height and distance to solve the problem. We will be using trigonometry to further simplify the solution. We will be using the fact that the angle of inclination of the sun is the same for all objects at a particular time. We will start by finding the ratio , where p is perpendicular and B is base, from triangle ABC and then from triangle DEF. Equating these two ratios, we will be able to find the height of the tower.
Complete step-by-step solution:
Now we have been given a vertical pole of 6m which casts a shadow of 4m on the ground and at the same time, a tower casts a shadow 28m long.
We have let the angle of inclination be in . We know that .
Where P is perpendicular and B is base. Therefore,
…………………… (1)
Now, we will apply in . We know that
Now, we will substitute the value of from (1)
On cross multiply we have
Therefore, the height of tower DE=42.
Note: To solve these types of questions it is important to note the fact that the sun has the same angle of inclination for all objects at a particular time also one must know some important trigonometric formulae like . Students can also try using the Pythagoras theorem and finding the perpendicular from triangle ABC and proceed or they might try to compute the angle. But, this is not required here, since the angle for both the cases would be the same. So, they can directly apply the tangent ratio, equate them, and get the answer.
Complete step-by-step solution:
Now we have been given a vertical pole of 6m which casts a shadow of 4m on the ground and at the same time, a tower casts a shadow 28m long.

We have let the angle of inclination be
Where P is perpendicular and B is base. Therefore,
Now, we will apply
Now, we will substitute the value of
On cross multiply we have
Therefore, the height of tower DE=42.
Note: To solve these types of questions it is important to note the fact that the sun has the same angle of inclination for all objects at a particular time also one must know some important trigonometric formulae like
Recently Updated Pages
Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Biology: Engaging Questions & Answers for Success

Master Class 12 Physics: Engaging Questions & Answers for Success

Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Trending doubts
Which one is a true fish A Jellyfish B Starfish C Dogfish class 10 biology CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Which tributary of Indus originates from Himachal Pradesh class 10 social science CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Distinguish between ordinary light and laser light class 10 physics CBSE
