A geometry problem by Mason Frey
Geometry
Level
pending
If the cosine of theta equals 0.5, what is the tangent of theta, rounded to the nearest thousandth?
The answer is 1.732.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Step 1: Convert 0.5 to degrees using the inverse of cosine --> 60 degrees
Step 2: Create possible side lengths for the hypotenuse and adjacent side that correspond with the cosine of 0.5 --> Hypotenuse = 10, Adjacent = 5, for example
Step 3: Solve for the remaining side using the Pythagorean Theorem --> 5^2 + b^2 = 10^2 || 25 + b^2 = 100 || b^2 = 75 || b = sqrt(75) or approx. 8.66
Step 4: Divide the side you just solved by the adjacent side to get the tangent of theta --> sqrt(75) / 5 = approx. 1.732
Answer is 1.732