Note: Your teacher will grade your response to this question to ensure you receive proper credit for your answer.

Question

Find the value of x. AB=7. AC=9 angle B=90 degrees. Angle C=xRound to the nearest degree.

Answer 1

To find the value of x, we can use the Pythagorean theorem since angle B is 90 degrees, making triangle ABC a right triangle.

By using the Pythagorean theorem, we have:
AB^2 + AC^2 = BC^2
7^2 + 9^2 = BC^2
49 + 81 = BC^2
130 = BC^2
BC = √130

Now, we can use the sine function to find the value of angle C:
sin(C) = opposite/hypotenuse
sin(C) = AB/AC
sin(C) = 7/√130
sin(C) ≈ 0.465

To find the value of x, we can use the arcsin function:
x = arcsin(0.465)
x ≈ 28 degrees

Therefore, the value of x is approximately 28 degrees.