Question

Find the value of x to the nearest tenth

Answer 1

tan 48 = x / 7

so

x = tan 48 * 7

x= 1.1106 * 7

x = 7.7742

x = 7.8

answer

7.8

Answer 2

This problem can be solved with trigonometry. You need to pick the correct trig ratio, from sine, cosine, and tangent, to solve it.

This is how you decide which trig ratio to use. For the given angle of 48 degrees, the leg measuring 7 units is the adjacent leg. (Adjacent = next to the angle.) The leg measuring x units is the opposite leg. (Opposite = across from the angle.) The trig ratio that relates the lengths of the opposite leg and the adjacent leg is the tangent.

$\tan \theta = \dfrac{opp~leg}{adj~leg}$

$\tan 48^\circ = \dfrac{x}{7}$

$x = 7 \tan 48^\circ$

Now you use a calculator to find tan 48 = 1.1106, and multiply it by 7.

$x = 7.7743$

Answer: x = 7.8