Find the value of the variables. if the answer is not an integer, leave it in simplest radical form.

Explanation:

The short leg is given to be 9 units long. This side is opposite the smallest angle. The rule is that smallest side is opposite the smallest angle. The hypotenuse is twice as long as the short leg in a 30-60-90 triangle, so 2*9 = 18 is the hypotenuse.

The long leg is equal to sqrt(3) times the short leg

long leg = (short leg)*sqrt(3)

long leg = 9*sqrt(3)

You can use the pythagorean theorem with a = 9 and c = 18 to solve for b

a^2 + b^2 = c^2

9^2 + b^2 = 18^2

81 + b^2 = 324

b^2 = 324 - 81

b^2 = 243

b = sqrt(243)

b = sqrt(81*3)

b = sqrt(81)*sqrt(3)

b = 9*sqrt(3)

It's a longer way to get the same answer as above for the length of the long leg.

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°

step-by-step explanation:

if you meant, "on the way from (3, 2) to (3, 14):

x does not change; y increases by 12.

ensure that you have copied down this problem correctly.   .