Question

NEED HELP ASAP!! This is a trigonometry question and I really need help, I do not understand it at all. thank you.

Answer 1

Answer:

AD = 11.87

Step-by-step explanation:

So first we need to figure out the missing angles.

In ΔBCD, we have two angles given, 40° and 25°, since the angles of a triangle must equal 180°, we need to subtract the sum of these two angles from 180° to find the remaining angle: 180° - (40° + 25°) = 115°

Now we can find the remaining angles in ΔABD. To find ∠D, we can subtract the 115° on the other side from 180° because segment AC is a straight line, which is 180°. This makes that angle 65°. Following the same steps we did before, we can subtract the sum of the two angles in the triangle from 180° to find the remaining angle: 180° - (68° + 65°) = 47°

Now that we have found all the angles, we can start finding the lengths of the segments by using the identity $\frac{a}{sin(A)}=\frac{b}{sin(B)}=\frac{c}{sin(C)} =\frac{d}{sin(D)}$

So we only need one segment length, BD, in order to find segment AD. To find segment BD, we can use $\frac{b}{sin(B)}=\frac{c}{sin(C)}$, in this case  $\frac{DC}{sin(B)}=\frac{BD}{sin(C)}$

Solving this equation for BD, we get $\frac{DCsin(C)}{sin(B)}={BD}$

Plugging in the values we have we get $BD =\frac{15sin(25)}{sin(40)} =9.86$

Now we can go over to ΔABD and use $\frac{a}{sin(A)}=\frac{b}{sin(B)}$, in this case  $\frac{BD}{sin(A)}=\frac{AD}{sin(B)}$

Solving this equation for AD, we get $\frac{BDsin(B)}{sin(A)} =AD$

Plugging in the values we have we get $AD=\frac{9.36sin(68)}{sin(47)} =11.87$

Segment AD = 11.87