Question

Solve the triangle:

Answer 1

Answer: 101.6

Since we are trying to find the sides of both the triangles, we will need to use the Sin, Cos, & Tan trigonometry functions. There are 3 equations:

`Sin (Angle) = (Opposite)/(Hypotenuse) \\Cos (Angle) = (Adjacent)/(Hypotenuse) \\Tan (Angle) = (Opposite)/(Adjacent)`

For this triangle shown in the picture, we can infer that the 88 is OPPOSITE to the 60° and 30° angles. So we already have the opposite, and since we are trying to find the adjacent, we will use the formula that consists both opposite and adjacent, which is the following:

`Tan(Angle) = (Opposite)/(Adjacent)`

Since
`x` is only a part of the long triangle, we will subtract the small triangle's side from the big one, which will give us
`x\\`.

We can input our values to solve each triangle's side lengths.

(You have to use the calculator for these)

Small one:

`Tan(60) = (88)/(Adjacent)\\Adjacent = (88)/(Tan(60))\\Adjacent = (88√(3) )/(3) = 50.807 (3 d.p)`

Big one:

`Tan(30) = (88)/(Adjacent) \\Adjacent = (88)/(Tan(30)) \\Adjacent = 88√(3) = 152.420 (3d.p)`

Now, to calculate
`x` , we will subtracat the small one from the big one like this: (it is better to input the values with the surds and not the real numbers for accurate marks and calculations)

`88√(3) - (88√(3) )/(3) = 101.6 (1 d.p)`

That is the answer. If you did not understand it completely, please reach me back and I will help you :)