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In a right triangle, if the side opposite the angle A is 6 units and the side adjacent to the angle A is 8 units, what is the value of cos(A)?
- a)2/3
- b)3/4
- c)4/5
- d)5/6
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
In a right triangle, if the side opposite the angle A is 6 units and t...
cos(A) = adjacent/hypotenuse
= 8/10
= 4/5
= 8/10
= 4/5
Most Upvoted Answer
In a right triangle, if the side opposite the angle A is 6 units and t...
Given:
In a right triangle, the side opposite angle A is 6 units.
The side adjacent to angle A is 8 units.
To Find:
The value of cos(A).
Solution:
The cosine function is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.
Step 1: Identify the sides of the right triangle:
- The side opposite angle A is 6 units.
- The side adjacent to angle A is 8 units.
Step 2: Use the Pythagorean theorem to find the length of the hypotenuse:
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let the length of the hypotenuse be 'c'.
Then, according to the Pythagorean theorem, we have:
c² = (6²) + (8²)
c² = 36 + 64
c² = 100
c = √100
c = 10 units
Step 3: Apply the cosine function:
The cosine of angle A is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.
cos(A) = adjacent/hypotenuse
cos(A) = 8/10
Step 4: Simplify the ratio:
cos(A) = 4/5
Answer:
The value of cos(A) is 4/5, which corresponds to option 'C'.
In a right triangle, the side opposite angle A is 6 units.
The side adjacent to angle A is 8 units.
To Find:
The value of cos(A).
Solution:
The cosine function is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.
Step 1: Identify the sides of the right triangle:
- The side opposite angle A is 6 units.
- The side adjacent to angle A is 8 units.
Step 2: Use the Pythagorean theorem to find the length of the hypotenuse:
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let the length of the hypotenuse be 'c'.
Then, according to the Pythagorean theorem, we have:
c² = (6²) + (8²)
c² = 36 + 64
c² = 100
c = √100
c = 10 units
Step 3: Apply the cosine function:
The cosine of angle A is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.
cos(A) = adjacent/hypotenuse
cos(A) = 8/10
Step 4: Simplify the ratio:
cos(A) = 4/5
Answer:
The value of cos(A) is 4/5, which corresponds to option 'C'.
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Community Answer
In a right triangle, if the side opposite the angle A is 6 units and t...
cos(A) = adjacent/hypotenuse
= 8/10
= 4/5
= 8/10
= 4/5
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In a right triangle, if the side opposite the angle A is 6 units and the side adjacent to the angle A is 8 units, what is the value of cos(A)?a)2/3b)3/4c)4/5d)5/6Correct answer is option 'C'. Can you explain this answer?
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