Question Video: Finding the Unknown Length in a Right Triangle Using Trigonometry Where the Unknown Is on the Top of the Fraction | Nagwa Question Video: Finding the Unknown Length in a Right Triangle Using Trigonometry Where the Unknown Is on the Top of the Fraction | Nagwa

Question Video: Finding the Unknown Length in a Right Triangle Using Trigonometry Where the Unknown Is on the Top of the Fraction Mathematics • First Year of Secondary School

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Find 𝑥 in the given figure. Give your answer to two decimal places.

02:15

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.

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