Question

Use the triangle shown to find the ratios. cos(A) tan(c)

Answer 1

`\cos(A)=(10)/(26)=(5)/(13)`

`\cos(A)=(5)/(13)`

`\tan(C)=(10)/(24)=(5)/(12)[tex]</p><p>[tex]\tan(C)=(5)/(12)`

Explanation:

Soh Cah Toa is acronym used in mathematics to help students remember the trigonometric-right-triangle ratios for sine,cosine, and tangent.

Let's break it down.

Sine is opposite over hypotenuse.

Cosine is adjacent over hypotenuse.

Tangent is opposite over adjacent.

Opposite and adjacent change depending on from which angle of the right triangle you are looking.

So the first ratio is in terms of the angle A.

That means we are to label the opposite and adjacent based on the location of angle A.

The hypotenuse never changes; AC is the hypotenuse and has measurement 26 ft.

The opposite side to angle A is the side not touching angle A. That is the side CB and has measurement 24 ft.

The adjacent side to angle A is the side touching angle A that isn't the hypotenuse. So the side touching angle A that isn't the hypotenuse is AB which has measurement 10 ft.

`\sin(A)=\frac{\text{opposite}}{\text{hypotenuse}}=(24 ft)/(26 ft)=(24)/(26)=(12)/(13)`.

`\cos(A)=\frac{\text{adjacent}}{\text{hypotenuse}}=(10 ft)/(26 ft)=(10)/(26)=(5)/(13)`

`\tan(A)=\frac{\text{opposite}}{\text{adjacent}}=(24 ft)/(10 ft)=(24)/(10)=(12)/(5)`

So the second ratio is in terms of angle C>

That means we are to label the opposite and adjacent based on the location of angle C.

The hypotenuse never changes; AC is the hypotenuse and has measurement 26 ft.

The opposite side to angle C is the side not touching angle C. That is the side AB and has measurement 10 ft.

The adjacent side to angle C is the side touching angle C that isn't the hypotenuse. So the side touching angle C that isn't the hypotenuse is CB which has measurement 24 ft.

`\sin(C)=\frac{\text{opposite}}{\text{hypotenuse}}=(10 ft)/(26 ft)=(10)/(26)=(5)/(13)`.

`\cos(C)=\frac{\text{adjacent}}{\text{hypotenuse}}=(24 ft)/(26 ft)=(24)/(26)=(12)/(13)`

`\tan(C)=\frac{\text{opposite}}{\text{adjacent}}=(10 ft)/(24 ft)=(10)/(24)=(5)/(12)`

Answer 2

The other person who answered was right but on edgeunity it just changes it to cosA = 10/26 and tanC= 10/24