Search 83,021 tutors

Finding angles and sides using sin cosine and tangent functions

Use a calculator and trigonometric ratios to find each length. Round to nearest hundredth.

Given the size of one angle and the length of the opposite side, find all sides and angles.


1.) 62* and opposite side is 11 m

* <-- used as degree symbol

Since this is trigonometry we state the assumption that one of the angles is 90*

sin(x) = opposite ÷ hypotenuse
sin(62) = 11m ÷ hypotenuse

In your calculator type the following:

sin (should show result: 0.88294759285892694203217136031572)
1/x(reciprocal button) (should show result:
= (should show result: 12.458270557579430792500383280142)

This is the length of the hypotenuse

Now you have the length of the opposite side and the length of the hypotenuse to find the length of the third side you would do the following.

cos(x) = adjacent ÷ hypotenuse cos(62*) = adjacent ÷ 12.458270557579430792500383280142

0.46947156278589077595946228822784 x
12.458270557579430792500383280142 = adjacent

adjacent = 5.8488037482762662288350745902407

To check the work use the tangent function as follows

tan(x) = opposite ÷ adjacent
tan(62*) = 11 ÷ 5.8488037482762662288350745902407
tan(62*) = 1.8807264653463320123608375958293

In calculator
tan(x) = 1.8807264653463320123608375958293

The check works!
The three sides are:
hypotenuse: 12.458270557579430792500383280142
adjacent: 5.8488037482762662288350745902407
opposite: 11

The three angles are:

I hope you can do the rounding yourself. I always round at the end so there aren't rounding errors carried throughout the work.


Parley K.

CPA, Math, Science, Computers, Internet, QuickBooks and Business Tutor

100+ hours