Question

Help, I don’t understand this DeltaMath question

In ΔHIJ, the measure of ∠J=90°, the measure of ∠I=52°, and JH = 4.2 feet. Find the length of IJ to the nearest tenth of a foot.

Answer 1

I can use the angle and the length of JH to find the length of IJ.

To do this, I look at the relationship IJ and JH have to the 52 degree angle. JH is opposite to angle I, and IJ is adjacent to angle I. Because the two side lengths are opposite and adjacent, I use the tangent function to solve this.

Tangent of an angle = the length of the opposite side / the length of the adjacent side. This is just another way to say tan(x)=opposite/adjacent

Now I can fill in what I know...
tan(52)=4.2/x
Now, I want to isolate x.
tan(52) = 4.2/x
x(tan(52))=4.2
x=4.2/tan(52)

Now I put 4.2/tan(52) into a calculator and get x = 3.3 ft

Hope this helps!