ACTIVITY 1

Look at the infographs below and then draw observations from what you have seen.

Knowing Two Sides and the Included Angle

SSS Triangle

When we know two sides and the included angle (SAS), there is another formula (in fact three equivalent formulas) we can use.

Depending on which sides and angles we know, the formula can be written in three ways:

Area = 12ab sin C

Area = 12bc sin A

Area = 12ca sin B

SSS Triangle

There's also a formula to find the area of any triangle when we know the lengths of all three of its sides.

This can be found on the Heron's Formula .

Step 1: Calculate "s" (half of the triangles perimeter):

s = a+b+c2

Step 2: Then calculate the Area:

Two sides angle included.

trig area example

First of all, you must decide what you know.

You know angle C = 25º, and sides a = 7 and b = 10.

So let's get going:

Area =(½)ab sin C

Put in the values we know:½ × 7 × 10 × sin(25º)

Do some calculator work:35 × 0.4226...

Area = 14.8 to one decimal place

Step 1: s = 5+5+52 = 7.5
Step 2: A = √(7.5 × 2.5 × 2.5 × 2.5) = √(117.1875) = 10.825...

questions:

Use Heron's formula to find the area of a triangle of lengths 2, 3 and 3.

Give your answer in surd form.

√2

√3

√5

2√2