Final answer:
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.