Solving Right Triangles│Please Help!

Question

Find the missing pieces of the triangle. Round to the nearest tenth.

AB = ?

CB = ?

<C = ?

Image link - https://ibb.co/LJvSyrj

Answer 1

Angle C = 90, Angle B = 39, Angle A = 180-90-39 = 51

Now for the side lengths

Using trigonometric identities:

11/BC = OPP/ADJ = tan(39), BC = 11/tan(39)

11/AB = OPP/HYP = sin(39), AB = 11/sin(39)

or

Using law of sines:

The law of sines states that the ratio between the length of a side and the sine of the opposite angle is the same for all 3 sides.

AC/sin(39) = 11/sin(39)

The ratio between any side and its opposite angle must be 11/sin(39)

BC/sin(51) = 11/sin(39), BC = 11sin(51)/sin(39) = 11cos(39)/sin(39) = 11/tan(39)

AB/sin(90) = 11/sin(39), AB = 11/sin(39)

Answer 2

We can start with finding angle A. Since angle C is 90°, the other 2 angles would also need to be 90°.

C by the drawing = 90°

A = 90-39 = 51°

sin 39 = 11/AB

AB = 11/sin 39

AB = 17.5

tan 39 = 11/BC

BC = 11/tan39

BC = 13.6