find ( mangle d ).\n\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\n(…

find ( mangle d ).\n\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\n( mangle d = square^circ )

find ( mangle d ).\n\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\n( mangle d = square^circ )

Answer

Answer:

52.1

Explanation:

Step1: Identify triangle type and sides

Triangle (BCD) is right - angled at (C). We know that in right - triangle (BCD), the side adjacent to (\angle D) is (CD = 7) and the hypotenuse (BD=9). We can use the cosine function to find the measure of (\angle D). The cosine of an angle (\theta) in a right - triangle is defined as (\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}).

Step2: Apply the cosine formula

For (\angle D), (\cos(\angle D)=\frac{CD}{BD}). Substituting (CD = 7) and (BD = 9) into the formula, we get (\cos(\angle D)=\frac{7}{9}).

Step3: Find the angle

To find (\angle D), we take the inverse cosine (also known as arccos) of (\frac{7}{9}). So, (\angle D=\arccos\left(\frac{7}{9}\right)). Using a calculator, (\arccos\left(\frac{7}{9}\right)\approx52.1^{\circ}) (rounded to the nearest tenth).