Question

What is the area of ΔABC such that b = 26 centimeters, c = 14 centimeters, and measure of angle A equals 20 degrees.

Answer 1

The calculations involve converting the angle to radians and substituting the values into the area formula. After calculations, the final answer is approximately 62.244 square centimeters the value closest to the given options is 64.240 square centimeters

Let's calculate the area of triangle ABC step by step.

Given:

Side b = 26 centimeters,

Side c = 14 centimeters,

Angle A = 20 degrees.

We'll use the formula for the area of a triangle:

Area = 1/2 * b * c * sin(A)

First, convert the angle from degrees to radians:

20 degrees * (π/180) ≈ 0.3491 radians

Now, substitute the values into the formula:

Area = 1/2 * 26 * 14 * sin(0.3491)

Using a calculator:

Area ≈ 1/2 * 26 * 14 * 0.342

Area ≈ 62.244 square centimeters

Answer 2

The given triangle is triangle ABC with sides b=26cm and c=14cm and angle A=20 degrees.

Recall the formula for the area of the triangle is

`A=(1)/(2)bc\sin A`

Substitute b=26cm , c=14cm and angle A=20 degrees, we get

`A=(1)/(2)*26*14*\sin 20^o`

`A=13*14*\sin 20^o`
`\text{ Use }\sin 20^o=0.34202014332.`

`A=13*14*0.34202014332`
`A=62.2476cm^2`

Hence the area of the given triangle is 62.248 square cm.