Question

Find the value of each variable help fast

Answer 1

Answer:

$a=10\sqrt{3}\ units$,$b=5\sqrt{3}\ units$,$c=15\ units$,$d=5\ units$

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

Find the value of b

In the right triangle BCD

$sin(60\°)=\frac{b}{10}$

$b=sin(60\°)(10)$

Remember that

$sin(60\°)=\frac{\sqrt{3}}{2}$

so

$b=\frac{\sqrt{3}}{2}(10)$

$b=5\sqrt{3}\ units$

step 2

Find the value of d

In the right triangle BCD

$cos(60\°)=\frac{d}{10}$

$d=cos(60\°)(10)$

Remember that

$cos(60\°)=\frac{1}{2}$

so

$d=\frac{1}{2}(10)$

$d=5\ units$

step 3

Find the value of a

In the right triangle ABD

$sin(30\°)=\frac{b}{a}$

$a=\frac{b}{sin(30\°)}$

Remember that

$sin(30\°)=\frac{1}{2}$

$b=5\sqrt{3}\ units$

so

$a=\frac{5\sqrt{3}}{(1/2)}$

$a=10\sqrt{3}\ units$

step 4

Find the value of c

In the right triangle ABD

$cos(30\°)=\frac{c}{a}$

$c=(a)cos(30\°)$

Remember that

$cos(30\°)=\frac{\sqrt{3}}{2}$

$a=10\sqrt{3}\ units$

substitute

$c=(10\sqrt{3})\frac{\sqrt{3}}{2}$

$c=15\ units$

therefore

$a=10\sqrt{3}\ units$

$b=5\sqrt{3}\ units$

$c=15\ units$

$d=5\ units$