Question

((Image Included))

Answer 1

Answer: 204.12 inches

Step-by-step explanation:

We can find the lengths of the unknown sides by applying these identities:

$tan\alpha=\frac{opposite}{adjacent}\\\\sin\alpha=\frac{opposite}{hypotenuse}$

Observe the image attached. To find "a" we need to substitute the following values into $tan\alpha=\frac{opposite}{adjacent}$:

$\alpha=30\°\\opposite=x=27\\adjacent=a$

And solve for "a":

$tan(30\°)=\frac{27}{a}\\\\a=\frac{27}{tan(30\°)}\\\\a=46.76\ inches$

To find "b" we need to substitute the following values into $sin\alpha=\frac{opposite}{hypotenuse}$:

$\alpha=30\°\\opposite=x=27\\hypotenuse=b$

And solve for "b":

$sin(30\°)=\frac{27}{b}\\\\b=\frac{27}{sin(30\°)}\\\\b=54 inches$

 To find "c" we need to substitute the following values into $sin\theta=\frac{opposite}{hypotenuse}$:

$\theta=45\°\\opposite=x=27\\hypotenuse=c$

And solve for "c":

$sin(45\°)=\frac{27}{c}\\\\c=\frac{27}{sin(45\°)}\\\\c=38.18 inches$

Since the triangle on the left is Isosceles, then:

$d=c= 38.18\ inches$

Therefore, the perimeter is:

$P=(46.76+54+2(38.18)+27)\ inches=204.12\ inches$

Answer 2

Answer:

=204.13 inches.

Step-by-step explanation:

Using the side x, we can use sine to find the hypotenuse of the triangle with the angle marked 30°.

Sin 30 =x/hypotenuse.

sin 30 = 27/hyp

hyp= 27/sin 30

=54 inches

We can also find the adjacent as follows.

Cos 30 = adjacent/ 54

Adjacent= 54 cos 30

=46.77 inches

Using the angles marked 45 we can find the hypotenuse of the isosceles triangle.

sin 45= x/hypotenuse

sin 45 =27/hypotenuse

hypotenuse = 27/sin 45

=38.18 inches

The hypotenuse of both the triangles making the isosceles triangle are 38.18 inches long.

Perimeter = 54+ 46.77+27+ 38.18+38.18

=204.13 inches.