Question

1. find the measure of side c.

triangle with vertices a, b, c; side ac = 4, side bc = 7, angle at c is 102°; multiple choice options: 8.5, 9.7, 10.3, 8.8

Explanation:

Step1: Apply Law of Cosines

$$c^2 = a^2 + b^2 - 2ab\cos(C)$$
Here, $a=7$, $b=4$, $C=102^\circ$

Step2: Calculate cosine of 102°

$\cos(102^\circ) \approx -0.2079$

Step3: Substitute values into formula

$$c^2 = 7^2 + 4^2 - 2(7)(4)(-0.2079)$$
$$c^2 = 49 + 16 + 11.6424$$
$$c^2 = 76.6424$$

Step4: Solve for c

$$c = \sqrt{76.6424} \approx 8.75 \approx 8.8$$

Answer:

8.8