The area of a triangle - Higher

The area of any triangle can be calculated using the formula:

\text{Area of a triangle} = \frac{1}{2} ab \sin{C}

To calculate the area of any triangle the lengths of two sides and the angle in between are required.

Example

Calculate the area of the triangle. Give the answer to 3 significant figures.

Triangle (ABC) area = 1 over 2 x bc x sinA

Use the formula:

\text{area of a triangle} = \frac{1}{2} bc \sin{A}

\text{area} = \frac{1}{2} \times 7.1 \times 5.2 \sin{42}

area = 12.4 cm2

It may be necessary to rearrange the formula if the area of the triangle is given and a length or an angle is to be calculated.

Question

The area of the triangle is 5.45 cm2. Calculate the size of the acute angle YXZ. Give the answer to the nearest degree.

Triangle (XYZ) with sides 3.2cm and 5.3cm

Use the formula:

\text{area of a triangle} = \frac{1}{2} ab \sin{C}

5.45 = \frac{1}{2} \times 5.3 \times 3.2 \sin{C}

5.45 = 8.48 \sin{C}

Rearrange the equation to make \sin{C} the subject.

Divide both sides by 8.48.

\sin{C} = 0.642688 \dotsc. Do not round this answer yet.

To calculate the angle use the inverse \sin button on the calculator ( \sin^{-1}).

C = 40°

The angle YXZ is 40°.

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