Question

Geometry, please answer question ASAP

Answer 1

B.

Explanation:

The ratio of the lengths of the sides of a 30-60-90 triangle is

1 : sqrt(3) : 2

From the 1 and 2, we see that the hypotenuse must be twice the length of the short leg.

From the 1 and sqrt(3) we see that the long leg is sqrt(3) times the length of the short leg.

Now we check for these two ratios in each choice.

A.

1 is twice 1/2. Check

sqrt(3)/2 is sqrt(3) times 2. Check

B.

10 is twice 5, not twice 5/2. This does not check.

C.

2sqrt(2) is twice sqrt(2). Check

sqrt(6) is 2sqrt(2) time sqrt(3). Check

D.

6 is twice 3. Check

3sqrt(3) is sqrt(3) times 3. Check

Answer: B.

Answer 2

B

Explanation:

Angle ratio = 30 : 60 : 90

Side ratio = x : x√3 : 2x

`A) x = (1)/(2)\\\\ \ x√(3 ) = (1)/(2)*√(3)=(√(3))/(2) \\\\2x = 2*(1)/(2)=1`

True

`C) x = √(2) \\\\x√(3)=√(2) *√(3) =√(2*3)=√(6)\\\\2x=2√(2) \\`

True

`D) \ x = 3\\\\x√(3)=3√(3)\\\\2x = 2*3 = 6`

True