Question

Work out the length of x in the triangle below

Answer 1

x = 12 m

Explanation:

We can draw a line from the top of the triangle to the bottom such that the line is perpendicular to the bottom line i.e the line with length 14m

So, then we get two right triangles.

Lets say the bottom length of the left one is y m, then the bottom length of the right one is 14 - y,

Now, we need to find the height,

Since the area is 42, we know from formula of area of triangle,

1/2(base)(height) = A,

height = 2A/base

height = 2(42)/(14)

height = 6 m

So, h = 6 m

Now, the triangle on the right has side lengths h=6 m and 14-y m

and the hypotenuse = x m

Since we have to find the length of x,

we can use SOHCAHTOA, in this case, we know the opposite and need to find the hypotenuse (we also know the angle 30)

so we get,

sin(30) = opposite/Hypotenuse

Hypotenuse = 6/sin(30)

Hypotenuse = x = 12 m