Question

In AEFG, e = 210 cm, f = 520 cm, and g = 510 cm. Find the measure of ∠G to the nearest degree.

a) 33°
b) 42°
c) 58°
d) 63°

Answer 1

In AEFG, e = 210 cm, f = 520 cm, and g = 510 cm, the measure of ∠G to the nearest degree is 42° (option B).

Step-by-step explanation:

In triangle AEFG, the measure of angle ∠G can be found using the Law of Cosines, which states that for any triangle ABC:

`\[c^2 = a^2 + b^2 - 2ab \cos(C)\]`

In this case, let (e = a), (f = b), and (g = c). The angle ∠G is opposite side (g). Rearranging the formula to solve for ∠G:

`\[\cos(G) = (a^2 + b^2 - c^2)/(2ab)\]`

Substitute the given values:

`\[\cos(G) = \frac{(210 \, \text{cm})^2 + (520 \, \text{cm})^2 - (510 \, \text{cm})^2}{2 * 210 \, \text{cm} * 520 \, \text{cm}}\]`

Now, find the arccosine (inverse cosine) to get the angle ∠G:

`\[G = \cos^(-1)\left(\frac{(210 \, \text{cm})^2 + (520 \, \text{cm})^2 - (510 \, \text{cm})^2}{2 * 210 \, \text{cm} * 520 \, \text{cm}}\right)\]`

Calculating this expression yields the measure of ∠G. Rounding to the nearest degree, the correct answer is 42° (option B).