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What is the value of sin60?
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What is the value of sin60?
Solution:
Given, sin 60°
Trigonometric ratio of 60°
Let's consider a right-angled triangle ABC where angle B=90° and angle A=60°. Let the length of side AB be 'a', side BC be 'b' and side AC be 'c'.
Now, using trigonometric ratios, we can write:
- Sin 60° = Perpendicular/Hypotenuse = AB/AC
- Cos 60° = Base/Hypotenuse = BC/AC
- Tan 60° = Perpendicular/Base = AB/BC
Calculation of the value of sin 60°
In triangle ABC, we know that angle B=90° and angle A=60°. Therefore, angle C=30° (sum of angles of a triangle is 180°).
Using the concept of trigonometric ratios, we can write:
sin 60° = AB/AC
Now, in triangle ABC:
BC = a and AC = 2a (as angle A = 60°, angle B = 90°, so angle C = 30°, which means that BC is half of AC)
Using Pythagoras theorem:
a² = (AC)² - (BC)²
a² = (2a)² - a²
3a² = 4a²
a² = 4a²/3
a = (√3/2)a
Therefore, AB = (√3/2)a and AC = 2a
sin 60° = AB/AC = (√3/2)a/2a = √3/2
Final Answer:
The value of sin 60° is √3/2.
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What is the value of sin60?
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What is the value of sin60? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about What is the value of sin60? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the value of sin60?.
What is the value of sin60? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about What is the value of sin60? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the value of sin60?.
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