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ABC is a triangle, right angled at A. If the length of hypotenuse is 2 √2 times the length of perpendicular from A on the hypotenuse, the other angles of the triangle are :
- a)22.5°, 67.5°
- b)30°, 60°
- c)45°, 45°
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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ABC is a triangle, right angled at A. If the length of hypotenuse is 2...
Let's use the Pythagorean theorem to solve for the other two sides of the triangle.
a² + b² = c²
Since the triangle is right-angled at A, we know that angle B is 90 degrees. Therefore, we can use trigonometry to find the values of sin B and cos B.
sin B = a/c
cos B = b/c
Since the length of the hypotenuse is 2, we have:
c = 2
sin B = a/2
cos B = b/2
Now we can use the Pythagorean theorem to solve for a and b.
a² + b² = c²
a² + b² = 2²
a² + b² = 4
We also know that:
sin² B + cos² B = 1
Substituting the values for sin B and cos B, we get:
(a/2)² + (b/2)² = 1
Simplifying this equation, we get:
a² + b² = 4
Multiplying both sides by 4, we get:
4a² + 4b² = 16
Substituting a² + b² = 4, we get:
4(4) = 16
16 = 16
Therefore, the values of a and b are:
a = sin B * c = (1/2) * 2 = 1
b = cos B * c = (√3/2) * 2 = √3
So the triangle ABC is a 30-60-90 degree triangle with sides of length 1, √3, and 2.
a² + b² = c²
Since the triangle is right-angled at A, we know that angle B is 90 degrees. Therefore, we can use trigonometry to find the values of sin B and cos B.
sin B = a/c
cos B = b/c
Since the length of the hypotenuse is 2, we have:
c = 2
sin B = a/2
cos B = b/2
Now we can use the Pythagorean theorem to solve for a and b.
a² + b² = c²
a² + b² = 2²
a² + b² = 4
We also know that:
sin² B + cos² B = 1
Substituting the values for sin B and cos B, we get:
(a/2)² + (b/2)² = 1
Simplifying this equation, we get:
a² + b² = 4
Multiplying both sides by 4, we get:
4a² + 4b² = 16
Substituting a² + b² = 4, we get:
4(4) = 16
16 = 16
Therefore, the values of a and b are:
a = sin B * c = (1/2) * 2 = 1
b = cos B * c = (√3/2) * 2 = √3
So the triangle ABC is a 30-60-90 degree triangle with sides of length 1, √3, and 2.
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ABC is a triangle, right angled at A. If the length of hypotenuse is 2 √2times the length of perpendicular from A on the hypotenuse, the other angles of the triangle are :a)22.5°, 67.5°b)30°, 60°c)45°, 45°d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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