Question

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

Answer 1

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.

Answer 2

Tan A = 3/4 = 0.75
so
angle A = tan^-1 ( 0.75 ) = 36.9

Answer 3

degrees (rounded to one decimal place).

Answer 4

or sin A = 3/5 = 0.6
A = 36.9

or cos A = 4/5 = 0.8
A = 36.9

Answer 5

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.

Answer 6

Nonsense !

Answer 7

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?

Answer 8

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

Answer 9

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.

Answer 10

Whew, another stressful morning :)

Answer 11

I'm sorry to hear that. Please let me know if there's anything more I can do to assist you.