Question

In ΔHIJ, the measure of ∠J=90°, the measure of ∠H=71°, and JH = 2 feet. Find the length of IJ to the nearest tenth of a foot.

Answer 1

Answer:

5.8ft

Step-by-step explanation:

Since one of the angle in ΔHIJ is 90°, the triangle is a right angled triangle.

Using the SOH, CAH, TOA identity in trigonometry.

Given ∠H=71°, ∠J=90°

∠I = 180-(90+71)

∠I = 180-161

∠I = 19°

Considering ∠I, the opposite side to the angle is JH. The side facing the right angle ∠J=90° will be the hypothenuse (HI).

Side JH which is he third side will be adjacent side.

Since JH = 2feet

Using TOA:

Tan∠I= Opposite/Adjacent

Tangent∠I = JH/IJ

Tan19° = 2/IJ

IJ = 2/tan19°

IJ = 5.8feet (to nearest tenth of a foot)