Question

Want an extra challenge? This screen is **optional**: 30° If you want more practice to really level up your Right Triangle Trig skills, see if you can solve for the missing sides of the Right Triangle pictured to the left. C a You can enter your results and check your work in the table below. 7 HINT: The side that is 7 units long is OPPOSITE the 30° angle. Length of Hypotenuse (c) Length of Other Leg (a) Did I Get Them Right?!

Answer 1

Answer:

c = 14

a = 7√3

Explanation:

To find the value of c, we will use the sin(30) because sin(30) is equal to the opposite side over the hypothenuse. So:

$\sin (30)=\frac{7}{c}$

Additionally, sin(30) is also equal to 0.5, so we can replace this value and solve for c:

$\begin{gathered} 0.5=\frac{7}{c} \\ 0.5c=7 \\ c=\frac{7}{0.5} \\ c=14 \end{gathered}$

Therefore, the length of the hypotenuse (c) is 7.

Now, we can calculate the length of the other leg using the Pythagorean theorem, where:

$a=\sqrt[]{c^2-7^2}^{}$

So, replacing the value of c by 14, we get:

$\begin{gathered} a=\sqrt[]{14^2-7^2} \\ a=\sqrt[]{196-49} \\ a=\sqrt[]{147} \\ a=\sqrt[]{49\cdot3} \\ a=7\sqrt[]{3} \end{gathered}$

Therefore, the length of the other leg (a) is 7√3