Question

In ΔHIJ, the measure of ∠J=90°, the measure of ∠I=29°, and JH = 88 feet. Find the length of IJ to the nearest tenth of a foot.

Answer 1

it's 158.8

Explanation:

Answer 2

We have been given that in ΔHIJ, the measure of ∠J=90°, the measure of ∠I=29°, and JH = 88 feet. We are asked to find the length of IJ to the nearest tenth of a foot.

First of all, we will draw a right triangle using our given information as shown in the attachment.

We can see that in triangle HIJ, the side IJ is adjacent side to angle I and JH is opposite side to angle I.

We know that tangent relates opposite side of right triangle to adjacent side.

`\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}`

`\text{tan}(29^(\circ))=(88)/(IJ)`

`IJ=\frac{88}{\text{tan}(29^(\circ))}`

`IJ=(88)/(0.554309051453)`

`IJ=158.7562024638191237`

Upon rounding to nearest tenth, we will get:

`IJ\approx 158.8`

Therefore, the length of the side IJ is approximately 258.8 units.