Question

using algebra find the value of each variable. write answers in simplest radical form. 16. a right triangle with a 30° angle, hypotenuse 10, opposite side to 30° is c, adjacent side is d

Explanation:

Step1: Identify side roles in 30-60-90 triangle

In a 30-60-90 right triangle, the hypotenuse is 2 times the shorter leg (opposite 30°). Here, hypotenuse = 10, shorter leg = $c$.
$\text{Hypotenuse} = 2 \times \text{Shorter Leg}$
$10 = 2c$

Step2: Solve for $c$

Rearrange to isolate $c$:
$c = \frac{10}{2} = 5$

Step3: Solve for longer leg $d$

The longer leg (opposite 60°) is $\sqrt{3}$ times the shorter leg.
$d = c \times \sqrt{3}$
$d = 5\sqrt{3}$

Answer:

$c = 5$, $d = 5\sqrt{3}$