Solved Examples on Cos 30 Degrees
Example 1: In a right-angled triangle, the base to the angle of 30° is 9m. Find the length of the Hypotenuse.
Solution:
Given: Base = 9m
Cos = √3/2
⇒ B/H = √3/2
⇒ 9/H = √3/2
⇒ H = (9 × 2) / √3
⇒ H = 6√3m
Example 2: In a right-angled triangle, the hypotenuse is 16m. and one angle is 30°, find the other two sides of the triangle.
Solution:
Given, Hypotenuse = 16, angle = 30°
Cos 30 = B/H
⇒ B/H = √3/2
⇒ B/16 = √3/2
⇒ B = 8√3m
Third side is calculated using Pythagoras theorem.
P2 + B2 = H2
⇒ P2 + (8√3)2 = 162
⇒ P2 + 192 = 256
⇒ P2 = 64
⇒ p = 8m
Sides of triangle are – 8m, 8√3m, 16m.
Example 3: Find the value of 4cos 30°/sin 30°.
Solution:
The value of cos 30° in fractions is √3/2, and the value of sin 30 in fractions is 1/2. Therefore, it can be written as,
4 cos 30°/sin 30° = 4[√3/2 × 2] = 4 × √3 = 4√3
Example 4: Find the value of sin 60° multiplied by cos 30°.
Solution:
The value of cos 30° in fractions is √3/2, and the value of sin 60° in fractions is √3/2. Therefore, it can be written as,
sin 60° × cos 30° = [√3/2 × √3/2]
⇒ sin 60° × cos 30° = 3/4
Cos 30 Degrees
Cos 30 Degrees: The value of cos 30 degrees in trigonometry is √3/2. In a right-angled triangle, cosine is the ratio of the base and hypotenuse. When the angle of the right-angled triangle is 30°, cos 30° is required. In fraction form, cos 30° is √3/2; in decimal form, the value is 0.8660.
Let’s understand how the value of cos 30° is obtained with examples.
Table of Content
- What is the Value of Cos 30 Degrees?
- How to Find the Value of Cos 30 Degrees
- Cos 30 Degrees – Methods to Find
- Cos 30 Degrees in Terms of Trigonometric Functions
- Cos 30 Degrees Using Unit Circle
- Cos 30 Degrees Proof
- Theoretical Approach
- Practical Approach
- People Also Read:
- Solved Examples on Cos 30 Degrees