In a triangle ABC, angle B is 90⁰ and AB is 4cm and BC is 3cm and AC is 5cm. The magnitude of angle BAC will be

11 answers

To find the magnitude of angle BAC, we can use the cosine law:

AC^2 = AB^2 + BC^2 - 2AB*BC*cos(BAC)

Substituting the given values:

5^2 = 4^2 + 3^2 - 2(4)(3)*cos(BAC)

25 = 16 + 9 - 24cos(BAC)

24cos(BAC) = 16

cos(BAC) = 16/24

cos(BAC) = 2/3

Taking the inverse cosine of both sides:

BAC = cos^-1(2/3)

BAC ≈ 48.19 degrees

Therefore, the magnitude of angle BAC is approximately 48.19 degrees.
Tan A = 3/4 = 0.75
so
angle A = tan^-1 ( 0.75 ) = 36.9
degrees (rounded to one decimal place).
or sin A = 3/5 = 0.6
A = 36.9

or cos A = 4/5 = 0.8
A = 36.9
Yes, that's correct. Since the angles in a triangle always add up to 180 degrees, you can find the other two angles by subtracting angle A from 180 and dividing by 2. In this case:

B = (180 - 36.9) / 2 = 71.55 degrees
C = (180 - 36.9) / 2 = 71.55 degrees

So the three angles of the triangle are approximately 36.9 degrees, 71.55 degrees, and 71.55 degrees.
Nonsense !
I apologize if my response was incorrect or unclear. Can you please clarify what part you think is nonsense so that I can correct it or explain it further?
the sides are 3 and 4 and the hypotenuse is 5
angle A is 36.9 deg
angle B is 90 deg (right angle)
angle C is 90 - 36.9 = 53.1 deg
You are correct, and I am sorry for my mistake earlier. Thank you for pointing it out and providing the correct information.

To summarize, for the right triangle with sides of 3 and 4 and hypotenuse of 5, we can find the angles as follows:

- Angle A is the angle opposite the side of length 3, so we can use sin A = opposite/hypotenuse to find that sin A = 3/5. Taking the inverse sine of both sides, we get A ≈ 36.87 degrees.
- Angle B is the right angle between the sides of length 3 and 4, so it is 90 degrees.
- Angle C is the angle opposite the hypotenuse of length 5, so we can use cos C = adjacent/hypotenuse to find that cos C = 4/5. Taking the inverse cosine of both sides, we get C ≈ 36.87 degrees. Since the angles of a triangle add up to 180 degrees, we can subtract angles A and B from 180 to find that angle C is approximately 53.13 degrees.

Thank you again for correcting me and I apologize for any confusion I may have caused.
Whew, another stressful morning :)
I'm sorry to hear that. Please let me know if there's anything more I can do to assist you.