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π΄π΅πΆ is a triangle where π΅πΆ equals 15 centimeters, π΄πΆ equals 25 centimeters, angle πΆ is equal to 41 degrees.
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Find the area of π΄π΅πΆ giving your answer to three decimal places.
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So first of all, what Iβve done is drawing a little sketch to help us understand the problem.
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And then, Iβm gonna label it with the information weβve got.
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So weβve got that π΅πΆ is equal to 15 centimeters, π΄πΆ is 25 centimeters, and we also have angle πΆ which is equal to 41 degrees.
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Okay, great.
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So now we have a labeled diagram that can help us to solve the problem.
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Well, to solve the problem, what it wants us to actually find is the area of π΄π΅πΆ.
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And to help us do that, we actually have a formula.
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And the formula for an area of a triangle is that the area is equal to a half ππ sin πΆ.
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Well, if we clear things here for this formula is not to get hung up all about the letters.
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In our question, it actually works cause πΆ is the angle weβre given.
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And π and π are the sides opposite to our angles π΄ and π΅.
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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.
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Okay, great.
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So now letβs use our formula and solve the problem.
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Okay, the first stage is actually is gonna be substitute our values into a half ππ sign πΆ.
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And actually itβs gonna work, like we said, because weβve got two sides and the angle between them.
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So this is gonna give us that the area π΄π΅πΆ is equal to a half multiplied by 15 multiplied by 25 and then multiplied by the sine of 41 degrees.
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Now, before we carry out the calculation to solve this, quick tip is just to make sure that the calculator is in degrees.
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So make sure that on the display you have a deg or a d so that that way, we know weβre gonna get the correct answer.
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Okay, so now when we calculate using our calculator in degrees, we get that the area π΄π΅πΆ is equal to 123.0110679.
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Okay, one more step left to do.
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Because if we take a look at the question, it wants us to leave our answer to three decimal places.
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So we need to do a bit of rounding here.
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So therefore, we can say that the area of triangle π΄π΅πΆ is equal to 123.011 centimeters squared, to three decimal places.