Find the area of an isosceles triangle with two sides being 1 and an angle A being 30 degrees.

AdminMod2
Aug 9, 2017

#4**+1 **

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. |

\(A_\triangle=\frac{1}{4}units^2=0.25units^2\) | |

TheXSquaredFactor
Aug 9, 2017

#2**0 **

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 \(\angle A\)?

TheXSquaredFactor
Aug 9, 2017

#4**+1 **

Best Answer

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. |

\(A_\triangle=\frac{1}{4}units^2=0.25units^2\) | |

TheXSquaredFactor
Aug 9, 2017