Find the best tutors and institutes for Class 10 Tuition
Q6:
A $1.5$ m tall boy is standing at some distance from a $30$ m tall building. The angle of elevation from his eyes to the top of the building increases from $30°$ to $60°$ as he walks towards the building. Find the distance he walked towards the building.
Solution :
Given:
- Height of the building ($AB$) = $30$ m.
- Height of the boy ($ED = FC$) = $1.5$ m.
- Initial angle of elevation ($\angle AEF$) = $30^\circ$.
- Final angle of elevation ($\angle ADF$) = $60^\circ$.
To find:
The distance the boy walked towards the building, which is the distance $EF$.
Step 1: Determine the height of the triangle above the boy's eye level.
Let the building be $AB$ and the boy's positions be $EF$ and $DC$. The height of the building $AB = 30$ m. Since the boy is $1.5$ m tall, the height of the triangle $AF$ (where $F$ is the point on $AB$ at the eye level of the boy) is:
$AF = AB - FB = 30 - 1.5 = 28.5$ m.
Step 2: Define the variables for the horizontal distances.
Let $DF = x$ and $EF = y$. We need to find $x$.
Step 3: Apply trigonometry in $\triangle ADF$.
In the right-angled triangle $\triangle ADF$, the angle of elevation is $60^\circ$.
Using the tangent ratio: $\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}$
$\tan(60^\circ) = \frac{AF}{DF}$
Since $\tan(60^\circ) = \sqrt{3}$:
$\sqrt{3} = \frac{28.5}{x}$
$x = \frac{28.5}{\sqrt{3}}$
Rationalizing the denominator: $x = \frac{28.5 \times \sqrt{3}}{3} = 9.5\sqrt{3}$ m.
Step 4: Apply trigonometry in $\triangle AEF$.
In the right-angled triangle $\triangle AEF$, the angle of elevation is $30^\circ$.
$\tan(30^\circ) = \frac{AF}{EF} = \frac{AF}{ED + DF}$
Since $\tan(30^\circ) = \frac{1}{\sqrt{3}}$:
$\frac{1}{\sqrt{3}} = \frac{28.5}{y + x}$
$y + x = 28.5\sqrt{3}$
Step 5: Calculate the distance walked ($y$).
$y = 28.5\sqrt{3} - x$
$y = 28.5\sqrt{3} - 9.5\sqrt{3}$
$y = 19\sqrt{3}$ m.
Final Answer: The distance the boy walked towards the building is $19\sqrt{3}$ m.
More Questions from Class 10 Mathematics Applications of Trigonometry EXERCISE 9.1
- Q1: A circus artist is climbing a $20$ m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is $30°$ (see Fig. 9.11).
- Q10: Two poles of equal heights are standing opposite each other on either side of the road, which is $80$ m wide. From a point between them on the road, the angles of elevation of the top of the poles are $60°$ and $30°$, respectively. Find the height of the poles and the distances of the point from the poles.
- Q11: A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is $60°$. From another point $20$ m away from this point on the line joing this point to the foot of the tower, the angle of elevation of the top of the tower is $30°$ (see Fig. 9.12). Find the height of the tower and the width of the canal.
- Q12: From the top of a $7$ m high building, the angle of elevation of the top of a cable tower is $60°$ and the angle of depression of its foot is $45°$. Determine the height of the tower.
- Q13: As observed from the top of a $75$ m high lighthouse from the sea-level, the angles of depression of two ships are $30°$ and $45°$. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
- Q14: A $1.2$ m tall girl spots a balloon moving with the wind in a horizontal line at a height of $88.2$ m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is $60°$. After some time, the angle of elevation reduces to $30°$ (see Fig. 9.13). Find the distance travelled by the balloon during the interval.
- Q15: A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of $30°$, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be $60°$. Find the time taken by the car to reach the foot of the tower from this point.
- Q2: A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle $30°$ with it. The distance between the foot of the tree to the point where the top touches the ground is $8$ m. Find the height of the tree.
- Q3: A contractor plans to install two slides for the children to play in a park. For the children below the age of $5$ years, she prefers to have a slide whose top is at a height of $1.5$ m, and is inclined at an angle of $30°$ to the ground, whereas for elder children, she wants to have a steep slide at a height of $3$m, and inclined at an angle of $60°$ to the ground. What should be the length of the slide in each case?
- Q4: The angle of elevation of the top of a tower from a point on the ground, which is $30$ m away from the foot of the tower, is $30°$. Find the height of the tower.
- Q5: A kite is flying at a height of $60$ m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is $60°$. Find the length of the string, assuming that there is no slack in the string.
- Q7: From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a $20$ m high building are $45°$ and $60°$ respectively. Find the height of the tower.
- Q8: A statue, $1.6$ m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is $60°$ and from the same point the angle of elevation of the top of the pedestal is $45°$. Find the height of the pedestal.
- Q9: The angle of elevation of the top of a building from the foot of the tower is $30°$ and the angle of elevation of the top of the tower from the foot of the building is $60°$. If the tower is $50$ m high, find the height of the building.
CBSE Solutions for Class 10 Mathematics Applications of Trigonometry
Chapters in CBSE - Class 10 Mathematics
Top Tutors who teach Applications of Trigonometry
Super Tutor
Kodambakkam, Chennai
15 yrs of
Exp
57 students
3901 hrs of classes completed
800
per hour
Online Classes
With a decade of experience in teaching mathematics, physics, and chemistry for students from grades 8 through 12 across CBSE, IB, and ICSE boards, I offer a comprehensive educational approach that caters to a diverse range of curricula and learning needs. My academic background includes a BE and an MBA, equipping me with both technical and managerial skills that enhance my teaching methodology. Throughout my career, I have specialized in home tutoring, where I have developed a personalized approach to education that focuses on each student's unique needs and strengths. My sessions are designed to be interactive and engaging, fostering a learning environment where students feel supported and motivated. I conduct both online and offline classes, each lasting one hour, and utilize a variety of teaching tools to facilitate learning. I employ a whiteboard to visually explain concepts and provide question papers to help students practice and prepare for their exams. This hands-on approach ensures that students not only understand theoretical concepts but also develop problem-solving skills and confidence in their subjects. My commitment to delivering high-quality education and my extensive experience make me well-suited to guide students through their academic journey, helping them achieve their full potential in mathematics, physics, and chemistry.
Shri Seshadri sir was able to break the jinx of my son not learning indefinitely, with his experience in smoothly sliding into a routine with such interactive, yet nonchalant transition for my son's education. Thankyou sir, thankyou UrbanPro.
Top Tutor
Mohkam Pur Kala, Dehradun
8 yrs of
Exp
1 student
Student's Home
Tutor's home
5 years experience in teaching in math and science
Top Tutor
Mahipalpur, Delhi
14 yrs of
Exp
Student's Home
As an experienced teacher for nine years, I have been teaching to make students interested in the subjects of Maths. My attitude is to help children improve in studies in the best possible way.
Top Tutor
Karampura, Delhi
10 yrs of
Exp
2500
per hour
Online Classes
Student's Home
I am an IIM Kashipur alumnus, passionate about guiding students to achieve their immediate and long-term goals. As a personal tutor and founder of the online educational startup ‘MinDely,’ I have gained deep insights into child psychology and student needs, allowing me to tailor my teaching methods accordingly. I design lesson plans based on each student's grasp of concepts, ensuring a student-friendly and easy-to-understand approach. My weekly tests provide valuable insights for parents to track their child’s progress. I take pride in the success of my students, many of whom have graduated from IITs, DTU, and NSIT.
Top Tutor
Malkajgiri D.D.Colony, Hyderabad
20 yrs of
Exp
2 students
1269 hrs of classes completed
400
per hour
Online Classes
I was teaching in Government and Government aided schools. I Providing supervision & consultation for students, in the form of academic advising, students’ support, recruitment, courses and programs. Also, participating in student & staff social and cultural activities. PPP Approach to make the students understand the topics. Unified Approach to make the students to work independently and collaboratively. Heuristic Approach to make the students to understand theories through lab practical. Use few other contemporary approaches not limited to Brain Storming, Mind Mapping, Concept Mapping, Snowballing etc.,
Find more Tutor for Applications of Trigonometry in your City
- Bangalore Mathematics Tutors
- Delhi Mathematics Tutors
- Chennai Mathematics Tutors
- Gurgaon Mathematics Tutors
- Noida Mathematics Tutors
- Hyderabad Mathematics Tutors
- Mumbai Mathematics Tutors
- Chandigarh Mathematics Tutors
- Pune Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Jaipur Mathematics Tutors
- Surat Mathematics Tutors
Download free CBSE - Class 10 Mathematics Applications of Trigonometry EXERCISE 9.1 worksheets
Download Now
