Question

A= 5.2 B=70

Work out the area of the triangle. Round your answer to 1 DP

Answer 1

8.7

Explanation:

Calculate the area of the triangle by using sine.

Area of Triangle

`A = (1)/(2) * \text{side} * \text{side} * sin(\theta)`

θ ... included angle between the two sides

We already have two sides a and another side which is congruent to a, making it isosceles triangle. But we don't have the included angle. The angle we need is the vertex angle of the isosceles triangle. Angle B is one of the base angles (two base angles are congruent) and it measures 70°.

Recall that angles in any triangle add up to 180°.

base angle + base angle + vertex angle = 180°

70° + 70° + vertex angle = 180°

vertex angle = 40°

Now we have all the information to use the formula!

`A = (1)/(2) * \text{side} * \text{side} * sin(\theta)`

`A = (1)/(2) * 5.2 \text{ cm} * 5.2 \text{ cm} * sin(40^\circ)`

`A = 13.52 \text{ cm}^2 * sin(40^\circ)`

`A \approx 8.6904 \text{ cm}^2`

Rounded to 1 DP:

`A = 8.7 \text{ cm}^2`