Use triangle ABC drawn below & only the sides labeled. Find the side of length AB in terms of side a, side b & angle C only. You will need to use both Soh-Cah-Toa and the Pythagorean Theorem to solve for side AB.

Step-by-step explanation:

Given:

The above triangle

Required

Solve for AB in terms of a, b and angle C

Considering right angled triangle BOC where O is the point between b-x and x

From BOC, we have that:

Make h the subject:

Also, in BOC (Using Pythagoras)

Make the subject

Substitute for h

becomes

Factorize

In trigonometry:

So, we have that:

Take square roots of both sides

In triangle BOA, applying Pythagoras theorem, we have that:

Open bracket

Substitute and in

Open Bracket

Reorder

Factorize:

In trigonometry:

So, we have that:

Take square roots of both sides

where is the figure

the ratio of balloons to tables is 5: 2 and the constant variation is 5.

the equation is y=5x