Question

Please help it’s finding sin C , cos C and tan C

Answer 1

The given triangle has a right angle.

We use the mnemonics SOH-CAH-TOA.

1i) $\sin C =\frac{Opposite}{Hypotenuse}$,$\implies \sin C =\frac{30}{34}$,$\implies \sin C =\frac{15}{17}$

ii) $\cos C =\frac{Adjacent}{Hypotenuse}$,$\implies \cos C =\frac{16}{34}$,$\implies \cos C =\frac{8}{17}$

$\tan C =\frac{Opposite}{Adjacent}$,$\implies \tan C =\frac{30}{16}$,$\implies \tan C =\frac{15}{8}$

2. We want to find the hypotenuse.

We know an angle to be 23 degrees.

We were also given the side opposite to this angle to be 1200km.

Therefore we use the sine ratio.

Answer 2

Answer:

1) sin C = 30 / 34

cos C = 16/34

tan C = 30/16

2) The value of x = 1304.34

Step-by-step explanation:

1.

In a right angled triangle, we have perpendicular, hypotenuse and base.

The hypotenuse is the longest side and opposite to the right angle. the side having 90 degree angle is perpendicular.

Applying formulas we can find the values:

the formulas are : cos (Ф) = Base / hypotenuse

sin (Ф) = Perpendicular / hypotenuse

tan (Ф) = Perpendicular / Base

Putting values in the formula from figure:

sin C = Perpendicular / Hypotenuse

sin C = 30 / 34

cos C = Base / Hypotenuse

cos C = 16/34

tan C = Perpendicular / Base

tan C = 30/16

2.

We need to find the hypotenuse of the given triangle, we are given base = 1200 m and the angle is 23°

We know, cos Ф = Base / Hypotenuse.

Solving this, We can find the value of x.

cos (23) = 1200 / x

x cos (23) = 1200

x (0.920) = 1200

x = 1200 / 0.920

x = 1304.34

The value of x = 1304.34