Question

find the value of x.
13
25°
17
x
answer: x =
units
question help: video

Explanation:

Step1: Apply Law of Cosines

The Law of Cosines states that for a triangle with sides $a$, $b$, $c$, and angle $\theta$ opposite side $c$, $c^2 = a^2 + b^2 - 2ab\cos\theta$. Here, $x$ is the side opposite the $25^\circ$ angle, so:
$$x^2 = 13^2 + 17^2 - 2(13)(17)\cos(25^\circ)$$

Step2: Calculate squared terms

Compute the squares and product:
$$13^2 = 169, \quad 17^2 = 289, \quad 2(13)(17)=442$$
$$x^2 = 169 + 289 - 442\cos(25^\circ)$$

Step3: Sum constants and compute cosine

Sum the constants, use $\cos(25^\circ)\approx0.9063$:
$$169+289=458$$
$$x^2 = 458 - 442(0.9063)$$
$$x^2 = 458 - 400.5846$$

Step4: Solve for x

Calculate the difference and take square root:
$$x^2 \approx 57.4154$$
$$x \approx \sqrt{57.4154}$$

Answer:

$x \approx 7.58$ units