Question

calculator
what is the value of x?
enter your answer as a decimal in the box. round only your final answer to the nearest tenth.
x = \boxed{} cm
(there is a triangle egf with angle at e is 40°, angle at g is 87°, side eg is 13 cm, side ef is x)

Explanation:

Step1: Find angle at F

First, calculate $\angle F$ using the triangle angle sum (total $180^\circ$):
$\angle F = 180^\circ - 40^\circ - 87^\circ = 53^\circ$

Step2: Apply Law of Sines

Set up the ratio for Law of Sines:
$$\frac{x}{\sin(87^\circ)} = \frac{13}{\sin(53^\circ)}$$

Step3: Solve for x

Rearrange to isolate $x$ and compute:
$x = \frac{13 \times \sin(87^\circ)}{\sin(53^\circ)}$
Calculate the sines: $\sin(87^\circ) \approx 0.9986$, $\sin(53^\circ) \approx 0.7986$
$x \approx \frac{13 \times 0.9986}{0.7986} \approx \frac{12.9818}{0.7986} \approx 16.255$

Step4: Round to nearest tenth

Round the result to one decimal place:
$x \approx 16.3$

Answer:

$16.3$ cm