Apply to Aakash iACST Scholarship Test 2024
NCERT Solutions for Exercise 8.1 Class 10 Maths Chapter 8 Introduction to Trigonometry are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. Class 10 maths ex 8.1 deal with the concept of trigonometry and trigonometric ratios. The Branch of Mathematics that deals with the measurement of sides and angles of a triangle is known as trigonometry. Trigonometric Ratios are nothing but the ratios of the sides of a right triangle with respect to its acute angles. Trigonometrically, there are six ratios.
NCERT solutions for exercise 8.1 Class 10 Maths chapter 8 Introduction to Trigonometry focuses on trigonometry and trigonometric ratios including sine, cosine, tangent, cosecant, secant and cotangent. 10th class Maths exercise 8.1 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.
Apply to Aakash iACST Scholarship Test 2024
Introduction to Trigonometry class 10 chapter 8 Exercise: 8.1
Q1 In , right-angled at
,
. Determine :
Answer:
We have,
In ,
B = 90, and the length of the base (AB) = 24 cm and length of perpendicular (BC) = 7 cm
So, by using Pythagoras theorem,
Therefore,
AC = 25 cm
Now,
(i)
(ii) For angle C, AB is perpendicular to the base (BC). Here B indicates to Base and P means perpendicular wrt angle C
So,
and
Answer:
We have, PQR is a right-angled triangle, length of PQ and PR are 12 cm and 13 cm respectively.
So, by using Pythagoras theorem,
Now, According to question,
=
= 5/12 - 5/12 = 0
Answer:
Suppose ABC is a right-angled triangle in which
and we have
So,
Let the length of AB be 4 unit and the length of BC = 3 unit So, by using Pythagoras theorem,
units
Therefore,
and
Answer:
We have,
It implies that In the triangle ABC in which . The length of AB be 8 units and the length of BC = 15 units
Now, by using Pythagoras theorem,
units
So,
and
Q5 Given calculate all other trigonometric ratios.
Answer:
We have,
It means the Hypotenuse of the triangle is 13 units and the base is 12 units.
Let ABC is a right-angled triangle in which B is 90 and AB is the base, BC is perpendicular height and AC is the hypotenuse.
By using Pythagoras theorem,
BC = 5 unit
Therefore,
Q6 If and
are acute angles such that
, then show that
.
Answer:
We have, A and B are two acute angles of triangle ABC and
According to question, In triangle ABC,
Therefore, A =
B [angle opposite to equal sides are equal]
Q7 If evaluate:
Answer:
Given that,
perpendicular (AB) = 8 units and Base (AB) = 7 units
Draw a right-angled triangle ABC in which
Now, By using Pythagoras theorem,
So,
and
Answer:
Given that,
ABC is a right-angled triangle in which and the length of the base AB is 4 units and length of perpendicular is 3 units
By using Pythagoras theorem, In triangle ABC,
AC = 5 units
So,
Put the values of above trigonometric ratios, we get;
LHS RHS
Q9 In triangle , right-angled at
, if
find the value of:
Answer:
Given a triangle ABC, right-angled at B and
According to question,
By using Pythagoras theorem,
AC = 2
Now,
Therefore,
Q10 In , right-angled at
,
and
. Determine the values of
Answer:
We have, PR + QR = 25 cm.............(i)
PQ = 5 cm
and
According to question,
In triangle PQR,
By using Pythagoras theorem,
PR - QR = 1........(ii)
From equation(i) and equation(ii), we get;
PR = 13 cm and QR = 12 cm.
therefore,
Q11 State whether the following are true or false. Justify your answer.
(i) The value of is always less than 1.
(ii) for some value of angle A.
(iii) is the abbreviation used for the cosecant of angle A.
(iv) is the product of cot and A.
(v) for some angle
Answer:
(i) False,
because , which is greater than 1
(ii) TRue,
because
(iii) False,
Because abbreviation is used for cosine A.
(iv) False,
because the term is a single term, not a product.
(v) False,
because lies between (-1 to +1) [
]
The NCERT solutions for Class 10 Maths exercise 8.1 also focused on the relationship between the trigonometric ratios. Exercise 8.1 Class 10 Maths consists of 11 questions based on trigonometric ratios and their relations. The sine is the ratio of the opposing side to the hypotenuse of a right-angle triangle.
The cosine is the ratio of the neighboring side to the hypotenuse of a right-angle triangle. The tangent is the ratio of the opposite side to the adjacent side of a right-angle triangle. The multiplicative inverse of sine is known as cosecant. Similarly, the multiplicative inverse of cosine is known as secant. The multiplicative inverse of the tangent is known as cotangent. Usage of Pythagoras theorem is also covered in exercise 8.1 Class 10 Maths. Students can use these Introduction to Trigonometry Class 10 notes to quick revision of the important concepts discussed in this chapter.
Also, see-
As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters
The three basic trigonometric ratios are sine, cosine and tangent.
The ratio of the opposite side to the hypotenuse of the right angle triangle is known as the sine.
Sin θ=opposite side/hypotenuse
Cos means Cosine is the ratio of Adjacent Side and Hypotenuse
tan θ=sin θ/cos θ
The multiplicative inverse of sine is known as the cosecant
The six trigonometric ratios are
Sine
Cosine
Tangent
Cotangent
Cosecant
Secant.
NCERT solutions for Class 10 Maths chapter 8 exercise 8. 1 consists of 11 Questions in which 7 are short answers, 3 of them are long answers and the remaining one is a short answer with reasoning and all the questions are based on trigonometric ratios.
Late Fee Application Date:22 July,2024 - 31 July,2024
Late Fee Application Date:22 July,2024 - 31 July,2024
Hello Aspirant, Hope your doing great, your question was incomplete and regarding what exam your asking.
Yes, scoring above 80% in ICSE Class 10 exams typically meets the requirements to get into the Commerce stream in Class 11th under the CBSE board . Admission criteria can vary between schools, so it is advisable to check the specific requirements of the intended CBSE school. Generally, a good academic record with a score above 80% in ICSE 10th result is considered strong for such transitions.
hello Zaid,
Yes, you can apply for 12th grade as a private candidate .You will need to follow the registration process and fulfill the eligibility criteria set by CBSE for private candidates.If you haven't given the 11th grade exam ,you would be able to appear for the 12th exam directly without having passed 11th grade. you will need to give certain tests in the school you are getting addmission to prove your eligibilty.
best of luck!
According to cbse norms candidates who have completed class 10th, class 11th, have a gap year or have failed class 12th can appear for admission in 12th class.for admission in cbse board you need to clear your 11th class first and you must have studied from CBSE board or any other recognized and equivalent board/school.
You are not eligible for cbse board but you can still do 12th from nios which allow candidates to take admission in 12th class as a private student without completing 11th.
Yes, you can definitely apply for diploma courses after passing 10th CBSE. In fact, there are many diploma programs designed specifically for students who have completed their 10th grade.
Generally, passing 10th CBSE with a minimum percentage (often 50%) is the basic eligibility for diploma courses. Some institutes might have specific subject requirements depending on the diploma specialization.
There is a wide range of diploma courses available in various fields like engineering (e.g., mechanical, civil, computer science), computer applications, animation, fashion design, hospitality management, and many more.
You can pursue diplomas at various institutions like:
Register for Tallentex '25 - One of The Biggest Talent Encouragement Exam
Get up to 90% scholarship on NEET, JEE & Foundation courses
As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters
As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters
Accepted by more than 11,000 universities in over 150 countries worldwide
Register now for PTE & Save 5% on English Proficiency Tests with ApplyShop Gift Cards