I know how to do it but don’t have a calculator with the trig option sin-1 so can someone help me

x = 4.9 cm

Step-by-step explanation:

Note that sin theta = (opp side) / (hypotenuse), and that:

hypotenuse      (opp side)

=

         1                sin theta

and so:

hypotenuse      (opp side)                                           4 cm

=  or  hypotenuse = = x

         1                sin theta                                     sin (55 degrees)

                     4 cm

Thus, x =   = x = 4.88 cm or (to 1 DP)        x = 4.9 cm

                    0.819

step-by-step explanation:

b and c

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°