Question Video: Using the Trigonometric Formula for Area of Triangles to Find the Area of a Triangle Mathematics

Video Transcript

𝐴𝐵𝐶 is a triangle where 𝐵𝐶 equals 15 centimeters, 𝐴𝐶 equals 25 centimeters, angle 𝐶 is equal to 41 degrees. Find the area of 𝐴𝐵𝐶 giving your answer to three decimal places.

So first of all, what I’ve done is drawing a little sketch to help us understand the problem. And then, I’m gonna label it with the information we’ve got. So we’ve got that 𝐵𝐶 is equal to 15 centimeters, 𝐴𝐶 is 25 centimeters, and we also have angle 𝐶 which is equal to 41 degrees. Okay, great. So now we have a labeled diagram that can help us to solve the problem.

Well, to solve the problem, what it wants us to actually find is the area of 𝐴𝐵𝐶. And to help us do that, we actually have a formula. And the formula for an area of a triangle is that the area is equal to a half 𝑎𝑏 sin 𝐶. Well, if we clear things here for this formula is not to get hung up all about the letters. In our question, it actually works cause 𝐶 is the angle we’re given. And 𝑎 and 𝑏 are the sides opposite to our angles 𝐴 and 𝐵. However, what it actually means, so what our formula means is, is that we have the area equal to a half multiplied by a side, multiplied by another side, and then multiplied by the sine of the angle between them.

Okay, great. So now let’s use our formula and solve the problem. Okay, the first stage is actually is gonna be substitute our values into a half 𝑎𝑏 sign 𝐶. And actually it’s gonna work, like we said, because we’ve got two sides and the angle between them. So this is gonna give us that the area 𝐴𝐵𝐶 is equal to a half multiplied by 15 multiplied by 25 and then multiplied by the sine of 41 degrees.

Now, before we carry out the calculation to solve this, quick tip is just to make sure that the calculator is in degrees. So make sure that on the display you have a deg or a d so that that way, we know we’re gonna get the correct answer.

Okay, so now when we calculate using our calculator in degrees, we get that the area 𝐴𝐵𝐶 is equal to 123.0110679. Okay, one more step left to do. Because if we take a look at the question, it wants us to leave our answer to three decimal places. So we need to do a bit of rounding here. So therefore, we can say that the area of triangle 𝐴𝐵𝐶 is equal to 123.011 centimeters squared, to three decimal places.