Please help ASAP
Trigonometry

Step-by-step explanation:

Use SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

7)

now decide which parts we know and what we want to slove for and pick the function that has those in it

we also know that small angle down at the point b/c we can use that the inside of trianle angles add to 180

180 = 75 + 90 + X

15° = X  

where x is the angle at that sharp point on the triangle

I want to use that 15° angle in one of the above formulas as it's Opposite of that side we want to know, and also adjcent to that side we know , so i'll pick TOA  since it's got all of those in it.  Opp = x for this triangle

Tan(15) =  Opp / 15

15* Tan(15) = Opp

4.0192 = Opp

so that's x  

x = 4.0162 units , what ever they are

8)

the angle is 43° and we know the adjacent side and we want the Hypotenuse , now i'll pic  CAH  since it's got those pieces in it

Cos(43)= 31 / Hyp

some algebra just to switch Hyp out of the denominator

Hyp = 31 / Cos(43)

some tapping on my calculator

Hyp = 41.714

That's x for the second triangle

x = 41.71 units , what ever they are

:)

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°

i believe the answer is c.