Can we use SOH-CAH-TOA for the following triangle?

NO! This triangle is NOT a right triangle. We must use either the sine or the cosine rule

How and why should a non-right triangle be labelled?

Capital letters are for angles and lower case letters for the sides. If an angle is labelled as A, then little "a" is always used for the side opposite (directly across from) it. ALWAYS label ALL sides and angles. People make silly mistakes by plugging in the wrong values into the sine and cosine rules because they got their sides and angles confused.

Can the sine rule be upside down?

Yes, both formats are equally valid:

What parts of a triangle does the sine rule involve?

The sine rule involves

2 sides & 2 angles

(only ONE unknown)

What's the cheat to know which angle goes in the cosine rule?

The angle must be "sandwiched in" between two known sides (inscribed).

What parts of a triangle does the cosine rule involve?

The cosine rule involves

3 sides & 1 angle

(you can only have ONE unknown)

Can I use A = bh/2 to find the area of this triangle?

No. We don't have the vertical height. For non right-angle triangles use:

How do you find the area of a triangle using sine?

###
The area of a triangle is half of the product of two sides and the sine of the included angle.

When can you use the cosine rule to solve problems involving triangles?

When the triangles give:

- two sides and the included angle

or

- three sides

What is the sine rule?

What is the cosine rule?

What rule would you use for this triangle?

What rule would you use for this triangle?

Hint: count how many "given" angles there are (even if they are only drawn in with no actual measures)

What rule would you use for this trianlge?

How would you find b?

How would you find angle B?

What is an "angle of depression"?

It's the angle between the ceiling and a downward line.

What is an "angle of elevation"?

It's the angle between the floor and an upward line.

What are angles of elevation and depression?