Question
25. In triangle ABC, angle B is 90° and AB is 20cm, BC is 15 cm and AC is 25 cm.
The magnitude of angle BAC will be:
A. 53,1° B. 48,6° C. 36,9°
Answers
GPT 3.5
To find the magnitude of angle BAC, we can use the trigonometric identity sine. In triangle ABC, we can use the sine function to relate the lengths of the sides to the angles.
sin(BAC) = opposite / hypotenuse
In this case, the opposite side of angle BAC is AB, which has a length of 20 cm, and the hypotenuse is AC, which has a length of 25 cm.
sin(BAC) = 20 / 25
Using a calculator, we can find the inverse sine of this value to find the magnitude of angle BAC:
BAC = sin^(-1)(20/25)
BAC ≈ 36.87°
Therefore, the magnitude of angle BAC is approximately 36.9°, which corresponds to option C.
sin(BAC) = opposite / hypotenuse
In this case, the opposite side of angle BAC is AB, which has a length of 20 cm, and the hypotenuse is AC, which has a length of 25 cm.
sin(BAC) = 20 / 25
Using a calculator, we can find the inverse sine of this value to find the magnitude of angle BAC:
BAC = sin^(-1)(20/25)
BAC ≈ 36.87°
Therefore, the magnitude of angle BAC is approximately 36.9°, which corresponds to option C.