Question

Given that 0 = 8 mm 15.5°, calculate the area of the triangle below. Give your answer to 2 d.p. 20 mm 13 mm

Not drawn accurately Values given are approximate​

Answer 1

The area of the triangle, given the side lengths and angle, is approximately 34.70 mm².

How to calculate the area of a triangle

To calculate the area of a triangle with the given side lengths and angle, we can use the formula:

Area = (1/2) * a * b * sin(
`\theta`)

In this case, let's label the sides of the triangle as follows:

a = 20 mm

b = 13 mm

c = 8 mm

And the given angle is
`\theta` = 15.5°.

Now calculate the area using the formula:

Area = (1/2) * a * b * sin(
`\theta`)

Area = (1/2) * 20 mm * 13 mm * sin(15.5°)

To perform the calculation, convert the angle from degrees to radians since the trigonometric functions typically work with radian measures.

We can use the conversion: 1° = π/180 radians.

Converting theta to radians:

`\theta`_radians = 15.5° * (π/180)

`\theta`_radians ≈ 0.2705 radians

Now substitute the values into the formula:

Area = (1/2) * 20 mm * 13 mm * sin(0.2705 radians)

Area ≈ 0.5 * 20 mm * 13 mm * 0.2669

Area ≈ 34.70 mm² (rounded to 2 decimal places)

Therefore, the area of the triangle, given the side lengths and angle, is approximately 34.70 mm².