Question

use the law of cosines to find the value of $cos\theta$. round your answer to two decimal places.
a. 1.23
b. 0.35
c. 0.84
d. 0.23

Explanation:

Step1: Recall Law of Cosines

For angle $\theta$ with adjacent sides $a=9.8$, $b=10.2$, opposite side $c=5.7$, the formula is:
$$\cos\theta = \frac{a^2 + b^2 - c^2}{2ab}$$

Step2: Substitute the given values

$$\cos\theta = \frac{9.8^2 + 10.2^2 - 5.7^2}{2 \times 9.8 \times 10.2}$$

Step3: Calculate each squared term

$9.8^2=96.04$, $10.2^2=104.04$, $5.7^2=32.49$

Step4: Compute numerator and denominator

Numerator: $96.04 + 104.04 - 32.49 = 167.59$
Denominator: $2 \times 9.8 \times 10.2 = 199.92$

Step5: Divide and round to two decimals

$$\cos\theta = \frac{167.59}{199.92} \approx 0.35$$

Answer:

B. 0.35