in δfgh, f = 200 cm, g = 880 cm and ∠h=149°. find the length of h, to the nearest centimeter. answer attempt…

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines for side $h$ (opposite $\angle H$) is: $$h^2 = f^2 + g^2 - 2fg\cos(H)$$ Substitute $f=200$, $g=880$, $H=149^\circ$: $$h^2 = 200^2 + 880^2 - 2(200)(880)\cos(149^\circ)$$

Step2: Calculate individual terms

First, compute the squares: $200^2 = 40000$, $880^2 = 774400$ Then compute the cosine term: $\cos(149^\circ) \approx -0.8572$ $$2(200)(880)\cos(149^\circ) = 352000(-0.8572) \approx -301734.4$$

Step3: Combine terms to find $h^2$

$$h^2 = 40000 + 774400 - (-301734.4) = 814400 + 301734.4 = 1116134.4$$

Step4: Solve for $h$

Take the square root of $h^2$: $$h = \sqrt{1116134.4} \approx 1056.47$$

Answer:

1056 cm