Find HG and HI. A. HG = 11/ square root 3 and HI = 7 square root 3
B. HG= 11 square root 3/3 and HI= 7 square root 3/3
C. HG= 11 square root 3 and HI = 23 square root 3
D. HG= 11 square root 3/3 and HI = 22 square root 3/3

 Choice D

HG= 11 square root 3/3 and HI = 22 square root 3/3

In other words,

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Explanation:

Let's say that x is the short leg and y is the long leg

For any 30-60-90 triangle, we have this connection:

The long leg y is exactly sqrt(3) times longer compared to the short leg x.

Let's solve for x and then plug in y = 11

Side HG, the shorter leg, has an exact length of

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Once we know the short leg, we double that expression to get the length of the hypotenuse. Like before, this only applies to 30-60-90 triangles.

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Since and , this shows that choice D is the final answer.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

ok then what happened.