Inaugurated by IN-SPACe
ISRO Registered Space Tutor
S6-SA2-0048
What is the Value of cos 60?
Grade Level:
Class 10
AI/ML, Physics, Biotechnology, Space Technology, Chemistry, Engineering, Medicine
Definition
What is it?
The value of cos 60 degrees is a specific ratio in a right-angled triangle. It represents the ratio of the length of the adjacent side to the length of the hypotenuse, when one of the acute angles is 60 degrees.
Simple Example
Quick Example
Imagine you're flying a kite. If the string makes an angle of 60 degrees with the ground, and the string is the hypotenuse, then the horizontal distance from you to the point directly below the kite is related to cos 60. The value of cos 60 helps us find this horizontal distance easily.
Worked Example
Step-by-Step
Let's find the value of cos 60 using a special right-angled triangle.
Step 1: Start with an equilateral triangle ABC with each side length equal to 2 units. All angles in an equilateral triangle are 60 degrees.
---
Step 2: Draw an altitude (height) AD from vertex A to side BC. This altitude bisects (cuts into half) the base BC and also bisects angle A.
---
Step 3: Now, consider the right-angled triangle ADB. The angle at B is 60 degrees, the angle at D is 90 degrees, and the angle at A (angle BAD) is 30 degrees (half of 60 degrees).
---
Step 4: In triangle ADB, the hypotenuse AB = 2 units. The side BD is half of BC, so BD = 1 unit (since BC = 2 units).
---
Step 5: Recall the definition of cosine: cos(angle) = (Adjacent Side) / (Hypotenuse).
-----
Step 6: For angle B (60 degrees) in triangle ADB, the adjacent side is BD and the hypotenuse is AB.
---
Step 7: Substitute the values: cos 60 = BD / AB = 1 / 2.
---
Answer: Therefore, the value of cos 60 degrees is 1/2.
Why It Matters
Understanding cos 60 is crucial for solving problems in Physics, like calculating forces or projectile motion, and in Engineering for designing structures. Engineers use these values to ensure buildings are stable, and scientists in Space Technology use them to calculate satellite trajectories, opening doors to careers in ISRO or DRDO.
Common Mistakes
MISTAKE: Confusing cos 60 with sin 60 or tan 60. | CORRECTION: Remember the SOH CAH TOA mnemonic: Cosine is Adjacent/Hypotenuse (CAH).
MISTAKE: Writing cos 60 as 0.6 instead of 1/2. | CORRECTION: While 0.5 is numerically correct, it's best to use the exact fractional form 1/2 unless asked for a decimal approximation, especially in exams.
MISTAKE: Assuming cos 60 is the same as cos 30. | CORRECTION: Cosine values change with the angle. Cos 60 = 1/2, but cos 30 = sqrt(3)/2. Always refer to the trigonometric table or derive it carefully.
Practice Questions
Try It Yourself
QUESTION: In a right-angled triangle, if the hypotenuse is 10 cm and one angle is 60 degrees, what is the length of the side adjacent to the 60-degree angle? | ANSWER: 5 cm
QUESTION: If cos x = 1/2, what is the value of x (in degrees) for 0 <= x <= 90? | ANSWER: 60 degrees
QUESTION: An electric pole is 20 meters tall. A wire is stretched from the top of the pole to a point on the ground, making an angle of 60 degrees with the ground. What is the distance from the base of the pole to the point where the wire touches the ground? (Hint: You'll need tan 60 or sin 60 first, then cos 60). | ANSWER: 20/sqrt(3) meters (approximately 11.55 meters)
MCQ
Quick Quiz
What is the value of cos 60 degrees?
sqrt(3)/2
2026-01-02T00:00:00.000Z
1
The Correct Answer Is:
B
Cos 60 degrees is a standard trigonometric value derived from a 30-60-90 right-angled triangle, where the adjacent side is half the hypotenuse. Options A, C, and D are values for other angles or trigonometric functions.
Real World Connection
In the Real World
Imagine you are watching a cricket match and a fielder throws the ball. To calculate how far the ball travels horizontally before landing, especially if it's thrown at a certain angle, engineers and sports analysts use trigonometric values like cos 60. This helps them predict trajectories and improve player performance, much like how data scientists use these concepts in sports analytics apps.
Key Vocabulary
Key Terms
TRIGONOMETRY: The branch of mathematics dealing with the relations of the sides and angles of triangles | COSINE: A trigonometric ratio of the adjacent side to the hypotenuse in a right-angled triangle | HYPOTENUSE: The longest side of a right-angled triangle, opposite the right angle | ADJACENT SIDE: The side next to a given angle in a right-angled triangle, not the hypotenuse | ACUTE ANGLE: An angle less than 90 degrees
What's Next
What to Learn Next
Great job understanding cos 60! Next, you should explore the values of sin 60 and tan 60. These concepts are closely related and will help you build a complete understanding of trigonometry, preparing you for more complex problems in Class 11 and 12.
