Question

Find x to the nearest tenth.

Answer 1

To solve triangles, you first need to establish the labels of the sides. Since you already have 15° for an angle, use that angle to label. The longest side is always the hypotenuse (across from the right angle). The one opposite your angle (5) is the opposite side, and the remaining one (x) is the adjacent.

Now, to find x, you need to set up a ratio involving it and your other given side, the opposite. The correct trig ratio for this is going to be Tangent ($\frac{Opposite}{Adjacent}$). Set the Tangent of your angle equal to its ratio.

tan(15) = $\frac{5}{x}$ Now, get x by itself and solve like a regular equation
x(tan(15)) = 5   Divide by tan(15)
x = $\frac{5}{tan(15)}$   Plug this into a calculator
x = 18.660

x ≈ 18.7

So, the correct answer is 2 .

Answer 2

The correct answer is 18.7.

So I kind of went an indirect way but I can explain it all. I ignored the 15°. The box in the right correct means that angle is 90°. Since a triangle is always 180°, I subtracted 90 and 15 from 180. That gives you 75°. Now that you know that you can use tangent from SOH CAH TOA. So... tan75= x/5 which turns into 5tan75°. Plug that into a calculator and you get 18.66 which rounds to 18.7.

If you need anymore help I'm here. Hope I helped :) Good luck!