Question

How can you determine the measure of an angle if you know the opposite side of the angle and the hypotenuse?

Answer 1

Answer:

Use sine rule.

Explanation:

$\begin{tabular}{|c|c|c|c|} \cline{1-2} \multicolumn{2}{|c|}{\bf {SOH CAH TOA Formula's}} \\ \cline{1-2} \cline{1-2} \rm{sine rule} & sin(\theta) \sf = opposite/hypotenuse \\ \cline{1-2} \rm{cosine rule} & cos(\theta) \sf = adjacent/hypotenuse \\\cline{1-2} \rm{tan rule} & tan(\theta) \sf = opposite/adjacent \\ \cline{1-2}\end{tabular}$

If opposite side of an angle and hypotenuse is given.

Use sine rule: sin(θ) = opposite/hypotenuse

For example:

Given that opposite of the angle is 10 cm and hypotenuse is 20 cm.

To find the angle:

sin(θ) = 10/20

θ = sin⁻¹(10/20)

θ = sin⁻¹(1/2)

θ =  30°

Answer 2

Several ways

You can use sin directly

As

• sinØ=Opposite/Hypotenuse

Then you can find Ø from it

Otherwise

You may find adjacent using Pythagorean theorem

Then you can use cos

• cosØ=Adjacent/Hypotenuse

You may use tan even

• tanØ=Opposite/Adjacent