Triangle Area edited

In the diagram above, if we know the lengths of 2 sides of a triangle and the measure of the included angle, then the area of the triangle can be found using the formula of $A_\triangle=\frac{1}{2}ab\sin C$ . Now, let's apply the formula!

$A_\triangle=\frac{1}{2}ab\sin C$	Plug in the the side lengths as a and b (order is immaterial) and the measure of the included angle as C.
$A_\triangle=\frac{1}{2}(1)(1)\sin 30^{\circ}$	Let's simplify the sin of 30 degrees. You may already be aware that $\sin 30^{\circ}=0.5$ .
$A_\triangle=\frac{1}{2}(1)(1)(0.5)$	If you multiply a number by 1, the number is itself.
$A_\triangle=\frac{1}{2}(0.5)$	(1/2)*0.5=1/4, or 0.25.
$A_\triangle=\frac{1}{4}units^2=0.25units^2$

TheXSquaredFactor Aug 9, 2017

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TheXSquaredFactor · Answer 1 · 2017-08-09T06:19:21

There is a formula to find the area of a triangle for this exact situation. I will use a picture to illustrate it:

Source: http://maths.nayland.school.nz/Year_12/AS_2.4_Trigonometry/Images/Pinboard_posters/ScreenShot043.gif

In the diagram above, if we know the lengths of 2 sides of a triangle and the measure of the included angle, then the area of the triangle can be found using the formula of $A_\triangle=\frac{1}{2}ab\sin C$ . Now, let's apply the formula!

$A_\triangle=\frac{1}{2}ab\sin C$	Plug in the the side lengths as a and b (order is immaterial) and the measure of the included angle as C.
$A_\triangle=\frac{1}{2}(1)(1)\sin 30^{\circ}$	Let's simplify the sin of 30 degrees. You may already be aware that $\sin 30^{\circ}=0.5$ .
$A_\triangle=\frac{1}{2}(1)(1)(0.5)$	If you multiply a number by 1, the number is itself.
$A_\triangle=\frac{1}{2}(0.5)$	(1/2)*0.5=1/4, or 0.25.
$A_\triangle=\frac{1}{4}units^2=0.25units^2$

Guest · Answer 2 · 2017-08-09T05:18:54

Look for the answer here:

http://web2.0calc.com/questions/triangle-area_3

TheXSquaredFactor · Answer 3 · 2017-08-09T06:01:57

I'm mildly glad that this question was answered previously because reference to $\angle A$ is still ambiguous; $\angle A$ can refer to $\angle CAD$ , $\angle CAB$ , $\angle BAD$ .

If you want to reference an angle that has several common vertices, it is impossible to determine which angle one is referring to. Solve the problem by using 3 letters as opposed to 1. Can you please clarify which angle is indeed $\angle A$ ?

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