# The ratio of interior angles of a triangle is1:5:6. the shortest side is 4m. what is the area of the triangle?

1
by roshielespenilla

2014-12-23T18:04:09+08:00
1:5:6 ration of a triangle will give you a set of angles which is 15 degrees, 75 degrees and 90 degrees -- which means that you have right triangle.
Being the smallest angle, 15 degrees is the side that is opposite to the 4m.
Making use of the trigonometric functions (the SOH-CAH-TOA thingy), you'll need to get the side that is opposite to the 75 degree-angle for the calculation of area.

To get the other leg:
Sine 15 degrees = 4m/ Hypotenuse, then you will just derive the formula of hypotenuse here and it will be Hypotenuse = 4m/sine 15 degrees
Cosine 15 degrees = Adjacent/ hypotenuse, then it will be hypotenuse = adjacent/cosine 15 degrees, but we already know the equivalent of hypotenuse so we will use it as (4m/sine 15 degrees = adjacent/cosine 15 degrees). Deriving the measure of the adjacent side, we will have 4(cosine 15 degrees)/ sine 15 degrees.
Which is equal to:

To get the area, we would just multiply the adjacent side to the 2m (because we already divided it by 2 so we would not need to after).

And we will arrive to  , however simplifying it could get us to  or approximation of 29.856 square meters.