Question

4 formula 0.5 points find the area of a rectangle with a width of 8 inches and a diagonal of 18 inches. round your answer to the nearest tenth if necessary, but do not include \square inches\ with your response. answer
5 formula 0.5 points given right triangle abc, where side \c\ is the hypotenuse, angle b measures 50 degrees, and side c measures 15 m, find the length of side b. be sure your calculator is in deg mode, and use the proper trig function on your calculator in the computation. round your answer to the nearest hundredth. answer

Explanation:

Question 4

Step1: Find the length of the rectangle

In a rectangle, the diagonal, length, and width form a right triangle. Using the Pythagorean theorem \( a^2 + b^2 = c^2 \), where \( c \) is the diagonal, \( b \) is the width, and \( a \) is the length. Let the length be \( l \), width \( w = 8 \), diagonal \( d = 18 \). So \( l^2 + 8^2 = 18^2 \).
\( l^2 = 18^2 - 8^2 = 324 - 64 = 260 \)
\( l = \sqrt{260} \approx 16.1245 \)

Step2: Calculate the area of the rectangle

The area of a rectangle is \( A = l \times w \). Substitute \( l \approx 16.1245 \) and \( w = 8 \).
\( A = 16.1245 \times 8 \approx 128.996 \approx 129.0 \) (rounded to the nearest tenth)

Step1: Identify the trigonometric ratio

In right triangle \( ABC \), angle \( B = 50^\circ \), hypotenuse \( c = 15 \) m, side \( b \) is opposite angle \( B \). The sine function is \( \sin(B) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{b}{c} \).

Step2: Solve for \( b \)

Rearrange the formula: \( b = c \times \sin(B) \). Substitute \( c = 15 \) and \( B = 50^\circ \).
\( b = 15 \times \sin(50^\circ) \). Using a calculator in degree mode, \( \sin(50^\circ) \approx 0.7660 \).
\( b \approx 15 \times 0.7660 = 11.49 \)

Answer:

129.0

Question 5