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Answer:

These are right triangles so we can use Pythagorean theorem to solve this.

the  Pythagorean theorem states that the hypotenuse of a right triangle, squared, is equal to the sum of the other 2 sides of the triangle, squared.

It can be expressed as so:

c^2=a^2+b^2 where c is the hypotenuse and a, b are the other 2 sides.

Therefore in number 11 6^2=x^2+y^2

36=x^2+y^2

for A, 3√3 / 2 is 2.59807621135 and y is 3. If we square both then they should equal 36 although if they don't then this answer is incorrect.

By doing this process for each answer you will see that

In D we finally see that the square root of 3 is 1.73205080757 and that number times 3 is 5.19615242271. y is 3 and 5.19615242271 squared comes out to 27 and 3 squared comes out to 9

27+9 = 36. Therefore by using the Pythagorean theorem, we found that D is correct

Because this involves a lot of typing and its 5:37 Am where i live ima let u do the next one alone but if u need help just follow my demonstration

Step-by-step explanation:

The sides of the first right-angle triangle is 3[tex]\sqrt{3}[/tex] , 3 and the sides of the second right-angle triangle is  [tex]\frac{7\sqrt{3}}{2}[/tex] and 7.

What is a right-angle triangle?

"A right triangle or right-angled triangle, or more formally an orthogonal triangle, is a triangle in which one angle is a right angle or two sides are perpendicular. "

For the 1st right-angle triangle, two angles are 90°, 60°.

Therefore, the other angle is 30°.

Now, sin 60° = [tex]\frac{x}{6}[/tex]

⇒ x = 6sin 60° = 6 × [tex]\frac{\sqrt{3}}{2}[/tex] = 3[tex]\sqrt{3}[/tex]

Again, cos 60° = [tex]\frac{y}{6}[/tex]

⇒ x = 6cos 60° = 6 × [tex]\frac{{1}}{2}[/tex] = 3

Therefore, the sides of the first triangle is 3 and 3[tex]\sqrt{3}[/tex].

For the 2nd right-angle triangle, two angles are 90°, 60°.

Therefore, the other angle is 30°.

Now, tan 60° = [tex]\frac{b}{\frac{7}{2}}[/tex]

⇒ b = [tex]\frac{7}{2}[/tex] ×tan 60° = [tex]\frac{7\sqrt{3}}{2}[/tex]

Again, sin 60° = [tex]\frac{b}{a}[/tex]

⇒ a = b/sin 60° = [tex]\frac{7\sqrt{3}}{2}[/tex] / [tex]\frac{\sqrt{3}}{2}[/tex] = 7.

Therefore, the sides of the second triangle is 7 and  [tex]\frac{7\sqrt{3}}{2}[/tex].

Learn more about a right-angle triangle here: https://brainly.com/question/13446090

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