Question

Anwser the question below Plz brailiest.

Answer 1

The area of a triangle =
`(1)/(2)` × the length of one side × the length of another side × sin(the angle between these two sides). For our example, because we know one side = 10 and the angle is 30° we will use these in our formula for 'easyness'.

Area of triangle =
`(1)/(2)bc \sin A` where A is the angle in-between the two sides b and c. (b=10, A = 30°, c=???)

We need to find c on your diagram and then we can use the formula above. We can use the sine rule to find the length of side c.


`(10)/(\sin 45) = (c)/(\sin C)`
We know the angles in a triangle add up to 180° which means angle C must equal 180° - 45° - 30° = 105° so
`(10)/(\sin 45) = (c)/(\sin 105) \Rightarrow c= (10)/(\sin45) * \sin105 = 13.66`
side c = 13.66 so

`Area = (1)/(2)bc\sin \Rightarrow A = (1)/(2) * 10 * 13.66 * \sin30=34.15`
Area = 34 square units (to nearest square unit)