Question

How do you find the area of this triangle?

Answer 1

96.6937 square units

Explanation:

To find the area of a triangle when two sides and the included angle are given, we can use the Sine Rule for the area of a triangle formula.

Sine Rule

`\boxed{\text{Area} = (1)/(2) ab\sin C}`

where:

• a and b are the sides.
• C is the included angle.

In this case:

• a = 27
• b = 22
• C = 19°

Substitute these values into the formula and calculate:

`\text{Area} = (1)/(2) * 27 * 22 * \sin(19^(\circ))`

`\text{Area} = 13.5 * 22 * \sin(19^(\circ))`

`\text{Area} = 297 \sin(19^(\circ))`

`\text{Area} =96.69374187...`

`\text{Area} =96.6937\; \rm square \; units\;(4\;d.p.)`

Therefore, the area of the triangle is approximately 96.6937 square units when rounded to four decimal places.