Question

In a right triangle ABC, where angle ACB is a right angle and angle BAC is unknown, side BC is six units and side AB is seven units, what is the measure of angle BAC rounded to the nearest hundredth?

Answer 1

To find the measure of angle BAC in a right triangle ABC, we can use the Pythagorean theorem and the sine function.

Step-by-step explanation:

In a right triangle ABC, where angle ACB is a right angle and angle BAC is unknown, we can use the Pythagorean theorem to find the measure of angle BAC.

The Pythagorean theorem states that 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.

In this case, AB^2 + BC^2 = AC^2. Substituting the given values, 7^2 + 6^2 = AC^2.

Solving for AC, we get AC = sqrt(49 + 36) = sqrt(85).

Now, we can use the sine function to find angle BAC. sine(BAC) = opposite/hypotenuse = BC/AC.

Substituting the values, sine(BAC) = 6/sqrt(85). Taking the inverse sine, we can find angle BAC.