Question

In ΔHIJ, the measure of ∠J=90°, the measure of ∠I=60°, and JH = 80 feet. Find the length of IJ to the nearest tenth of a foot.

Answer 1

IJ ≈ 46. 20 ft

Explanation:

The triangle is ΔHIJ . The measure of ∠J=90 , the measure of ∠I=60° , and JH = 80 ft. The length IJ can be calculated below.

The illustration above forms a right angle triangle at angle J. Therefore the triangle has an hypotenuse side, opposite side and adjacent side.

opposite side = JH= 80 ft

adjacent side = IJ = ?

hypotenuse side = HI

Using SOHCAHTOA principle

we want to find the adjacent side

tan 60° = opposite/adjacent

tan 60° = 80/IJ

cross multiply

IJ tan 60° = 80

divide both sides by tan 60°

IJ = 80/tan 60°

IJ = 80/1.73205080757

IJ = 46.1880215352

IJ ≈ 46. 20 ft