Find the best tutors and institutes for Class 10 Tuition
Q1(i):
In $\triangle ABC$, right-angled at $B$, $AB = 24$ cm, $BC = 7$ cm. Determine : (i) $\sin A, \cos A$
Solution :
Given: In $\triangle ABC$, $\angle B = 90^\circ$, $AB = 24\text{ cm}$, and $BC = 7\text{ cm}$.
To find: The values of $\sin A$ and $\cos A$.
Step 1: Determine the length of the hypotenuse ($AC$).
Since $\triangle ABC$ is a right-angled triangle, we apply the Pythagoras Theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
$AC^2 = AB^2 + BC^2$ [Pythagoras Theorem]
$AC^2 = (24)^2 + (7)^2$
$AC^2 = 576 + 49$
$AC^2 = 625$
$AC = \sqrt{625} = 25\text{ cm}$
Step 2: Define the trigonometric ratios for angle $A$.
For $\angle A$, the side opposite is $BC = 7\text{ cm}$, the side adjacent is $AB = 24\text{ cm}$, and the hypotenuse is $AC = 25\text{ cm}$.
The definitions of sine and cosine are:
$\sin A = \frac{\text{Opposite side}}{\text{Hypotenuse}} = \frac{BC}{AC}$
$\cos A = \frac{\text{Adjacent side}}{\text{Hypotenuse}} = \frac{AB}{AC}$
Step 3: Calculate the values.
Substituting the known lengths into the ratios:
$\sin A = \frac{7}{25}$
$\cos A = \frac{24}{25}$
Final Answer: $\sin A = \frac{7}{25}$ and $\cos A = \frac{24}{25}$
More Questions from Class 10 Mathematics Introduction to Trigonometry EXERCISE 8.1
- Q1(ii): In $\triangle ABC$, right-angled at $B$, $AB = 24$ cm, $BC = 7$ cm. Determine : (ii) $\sin C, \cos C$
- Q10: In $\triangle PQR$, right-angled at $Q$, $PR + QR = 25$ cm and $PQ = 5$ cm. Determine the values of $\sin P, \cos P$ and $\tan P$.
- Q11(i): State whether the following are true or false. Justify your answer. (i) The value of $\tan A$ is always less than 1.
- Q11(ii): State whether the following are true or false. Justify your answer. (ii) $\sec A = \frac{12}{5}$ for some value of angle $A$.
- Q11(iii): State whether the following are true or false. Justify your answer. (iii) $\cos A$ is the abbreviation used for the cosecant of angle $A$.
- Q11(iv): State whether the following are true or false. Justify your answer. (iv) $\cot A$ is the product of cot and $A$.
- Q11(v): State whether the following are true or false. Justify your answer. (v) $\sin \theta = \frac{4}{3}$ for some angle $\theta$.
- Q2: In Fig. 8.13, find $\tan P – \cot R$.
- Q3: If $\sin A = \frac{3}{4}$, calculate $\cos A$ and $\tan A$.
- Q4: Given $15 \cot A = 8$, find $\sin A$ and $\sec A$.
- Q5: Given $\sec \theta = \frac{13}{12}$, calculate all other trigonometric ratios.
- Q6: If $\angle A$ and $\angle B$ are acute angles such that $\cos A = \cos B$, then show that $\angle A = \angle B$.
- Q7(i): If $\cot \theta = \frac{7}{8}$, evaluate : (i) $\frac{(1 + \sin \theta) (1 - \sin \theta)}{(1 + \cos \theta) (1 - \cos \theta)}$
- Q7(ii): If $\cot \theta = \frac{7}{8}$, evaluate : (ii) $\cot^2 \theta$
- Q8: If $3 \cot A = 4$, check whether $\frac{1 - \tan^2 A}{1 + \tan^2 A} = \cos^2 A – \sin^2 A$ or not.
- Q9(i): In triangle ABC, right-angled at B, if $\tan A = \frac{1}{\sqrt{3}}$, find the value of: (i) $\sin A \cos C + \cos A \sin C$
- Q9(ii): In triangle ABC, right-angled at B, if $\tan A = \frac{1}{\sqrt{3}}$, find the value of: (ii) $\cos A \cos C – \sin A \sin C$
CBSE Solutions for Class 10 Mathematics Introduction to Trigonometry
Chapters in CBSE - Class 10 Mathematics
Top Tutors who teach Introduction to Trigonometry
I'm delighted to introduce myself as an experienced educator with a strong passion for teaching Mathematics and Science to students from 6th to 10th grade in both CBSE and ICSE boards. Educational Background: I hold a degree in BSc Physics, followed by an MSc and a B.Ed. My academic journey has equipped me with a deep understanding of the subjects and effective teaching methodologies. Passion for Teaching: Teaching is not just a profession for me; it's a lifelong passion that ignited during my younger days. The desire to contribute to society through education has been a driving force throughout my career. Teaching Experience: My journey in education began during my BSc days when I started tutoring younger students. Over the years, I've refined my teaching skills, working as a home tutor and gaining valuable experience in schools catering to both ICSE and CBSE curricula. Online Teaching Approach: In this digital age, I understand the importance of adapting to modern teaching methods. My online sessions are designed to be interactive, engaging, and conducive to effective learning. Each session lasts for an hour, during which I ensure a comprehensive coverage of the material, coupled with interactive discussions and lesson plans. Commitment to Excellence: My commitment is not just to impart knowledge but to foster a love for learning. I strive to create an environment where students not only understand the subjects but also develop critical thinking skills. If you're seeking a dedicated and passionate educator for your child's academic journey, I'm here to help. Let's embark on this learning adventure together!
Excellent Teacher. She explains the chemistry fundamentals with great clarity using periodic table simultaneously checking the understanding of the student. I wish I had this coaching for my son much earlier. Her passion for the subject is visible and gets reflected in my son’s grades.
I am good at teaching Mathematics. I have been teaching Mathematics for CBSE, state and ICSE syllabi. I mentor students for IIT foundation as well as academic syllabus (based on student requirement). I follow a systematic teaching methodology to make students thorough at the subject. 1. Explanation of basic concepts 2. Correlating the concepts with applications 3. Practice exercises and explanation 4. Home work 5. Assessment at the end of each chapter/topic 6. Teaching files are accessible to download anytime for future reference as I conduct online classes. My objective is to make student strong at fundamentals & confident in solving any difficulty level problem from the subject.
Love his teaching. He teaches very nicely. I understand the concept very well because of him. He is an excellent teacher. Thank you so much for your support.
Dedicated and passionate educator with over 10 years of experience teaching Mathematics and Science to students of Classes 8th to 12th across multiple boards — CBSE, ICSE, IGCSE, IB MYP, and IBDP. Founder of Ishaan Tuitions, Pune, specializing in personalized one-to-one coaching and small group sessions designed to strengthen conceptual understanding and academic performance. Expertise also includes preparing students for competitive examinations such as SAT and IIT-JEE Mains, with a strong record of improving analytical thinking and problem-solving abilities.
My experience is very good with sachin sir his way of teaching I love and my thanks to Urbanpro also to help me to take me to such a good teacher
I've taught at least 150 students of this Class till date ....online/offline together.
Very good teacher and friendly also. I have already join this sir's class. Very helpful teacher definitely. Thank you so much for your support. Highly recommended to all. Has good grip in the concept.
I was a student in one of the top colleges of Ludhiana. I have proficiency in English . I can teach all subjects to primary wing .
Find more Tutor for Introduction to 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
- Ghaziabad Mathematics Tutors
- Chandigarh Mathematics Tutors
- Pune Mathematics Tutors
- Jaipur Mathematics Tutors
- Surat Mathematics Tutors
Download free CBSE - Class 10 Mathematics Introduction to Trigonometry EXERCISE 8.1 worksheets
Download Now