Question

analyze the diagram below and complete the instructions that follow. find the value of z. round the answer to the nearest tenth, if needed. a. 9.5 b. 20.8 c. 29.6 d. 45.6

Explanation:

Step1: Find hypotenuse of big triangle

First, calculate the hypotenuse of the large right triangle using the Pythagorean theorem:
$$c = \sqrt{16^2 + 27^2} = \sqrt{256 + 729} = \sqrt{985} \approx 31.38$$

Step2: Use area equality to find z

The area of the large triangle can be calculated in two ways: $\frac{1}{2} \times 16 \times 27$ and $\frac{1}{2} \times \sqrt{985} \times z$. Set them equal:
$$\frac{1}{2} \times 16 \times 27 = \frac{1}{2} \times \sqrt{985} \times z$$
Simplify and solve for z:
$$z = \frac{16 \times 27}{\sqrt{985}} = \frac{432}{31.38} \approx 45.6$$

Answer:

D. 45.6