For this problem use the triangle in the figure. If a = 7 feet find b and c . Express the answers in simplest radical form.
A) $b = 7 \sqrt { 3 } \text { feet, } c = 14 \sqrt { 3 } \text { feet }$
B) $b = 14 \text { feet, } c = 14 \text { feet }$
C) $b = 7 \sqrt { 3 } \text { feet, } c = 14 \text { feet }$
D) $b = 7 \sqrt { 3 } \text { feet, } c = 7 \sqrt { 3 } \text { feet }$

Question

For this problem use the triangle in the figure. If a = 7 feet find b and c . Express the answers in simplest radical form. 
A) $b = 7 \sqrt { 3 } \text { feet, } c = 14 \sqrt { 3 } \text { feet }$ 
B) $b = 14 \text { feet, } c = 14 \text { feet }$ 
C) $b = 7 \sqrt { 3 } \text { feet, } c = 14 \text { feet }$ 
D) $b = 7 \sqrt { 3 } \text { feet, } c = 7 \sqrt { 3 } \text { feet }$

Quizplus · Accepted Answer

Using the Pythagorean Theorem, we have:

$b^2 + 7^2 = c^2$

Simplifying, we get:

$b^2 = c^2 - 49$

Now, looking at the triangle, we see that it is a 30-60-90 triangle. In such a triangle, the side opposite the 60 degree angle (which is side $b$ in this case) is always $\sqrt{3}$ times the length of the side opposite the 30 degree angle (which is side $a$ in this case). So, we have:

$b = 7\sqrt{3}$

Substituting this into our equation for $b^2$, we get:

$(7\sqrt{3})^2 = c^2 - 49$

Simplifying, we get:

$c^2 = 147 + 49 = 196$

Taking the square root, we get:

$c = 14$

So our final answer is:

$b = 7\sqrt{3}$

$c = 14$

Therefore, the best choice is C.

For This Problem Use the Triangle in the Figure b=73 feet, c=143 feet b = 7 \sqrt { 3 } \text { feet, } c = 14 \sqrt { 3 } \text { feet }b=73​ feet, c=143​ feet

For This Problem Use the Triangle in the Figure $b = 7 \sqrt { 3 } \text { feet, } c = 14 \sqrt { 3 } \text { feet }$