A building lot in a city is shaped as a 30°-60°-90° triangle, like the figure shown. The side opposite the 30° angle measures 41 feet. a. Find the length of the side of the lot opposite the 60° angle. Show how you know. b. Find the length of the hypotenuse of the triangular lot. Show how you know.
Accepted Solution
A:
You haven't shared the figure mentioned. However, we can still solve this problem.
If you have a 30-60-90 triangle, then the sides opposite these angles have basic lengths 1, sqrt(3) and 2. In other words, the side with length 2 is the hypotenuse and is opposite the right angle (90 deg).
Let's apply the Law of Sines:
a b c ------- = --------- = ----------- sin A sin B sin C
If a = 41 ft is opposite the 30 degre angle, then
41 ft x ---------- = ----------- sin 30 sin 60
Then x(sin 30) = (41 ft)(sin 60), or 41sqrt(3) x = --------------- = 82sqrt(3) 0.5
The hypotenuse could be found using a similar approach:
41 ft x ---------- = ----------- sin 30 sin 90
In this case x will represent the length of the hypotenuse.