Video Transcript
Find 𝑥 in the given figure. Give your answer to two decimal
places.
The first thing we notice is that
this is a right triangle. We know an angle and a side
length. And that means to solve the
problem, we’ll need to use the trigonometric ratios. We remember the acronym SOH CAH
TOA. sin of 𝜃 equals the opposite over
the hypotenuse, cos of 𝜃 equals the adjacent over the hypotenuse, and tan of 𝜃
equals the opposite over the adjacent. Our starting point is always the
angle concerned. We’re given the angle 68
degrees. And so we can label the opposite
side side 𝑥; the adjacent side, the side that’s 11; and the hypotenuse is always
the side opposite the right angle.
Once we’ve labeled these sides, we
see that we’re given the length of the adjacent side. And we’re interested in the length
of the opposite side. Since we’re dealing with the
opposite and the adjacent, we’ll be looking at the tangent ratio. Since the tan of 𝜃 equals the
opposite over the adjacent, we plug in 68 degrees for the angle. The opposite side is the side we’re
trying to find, 𝑥. And the adjacent side measures
11.
In order to solve for 𝑥, we need
to isolate it to get it by itself. We can do that by multiplying both
sides of this equation by 11. 11 times tan of 68 degrees will
equal the side length 𝑥. From here, to solve, we’ll need to
use a calculator. We’ll enter 11 times tan of 68
degrees, and it will give us 27.22595 continuing. If your calculator does not return
this value, you should check and make sure that it’s set to degree mode and not to
radians.
The missing side of 𝑥 is
27.22595. We want it correct to two decimal
places. To round to the second decimal
place, we look to the right. Since there’s a five in the third
decimal place, we need to round up. And we’ll get that 𝑥 equals
27.23. As we aren’t given any units, it’s
fine to leave it in this format. 𝑥 equals 27.23.
