Question

In AGHI, the measure of ZI=90', the measure of ZG-20', and IG = 98 feet. Find

the length of GH to the nearest tenth of a foot,
20
08

Answer 1

GH = 104.3 ft

Explanation:

You have a right triangle, so you can use a trig ratio: sine, cosine, or tangent.

You are given the measure of angle G and the length of leg IG. Side GH is the hypotenuse. For angle G, side IG is the adjacent leg. The trig ratio that relates the adjacent leg and the hypotenuse is the cosine.

`cos A = (adj)/(hyp)`

`cos G = (IG)/(GH)`

`cos 20^\circ = (98)/(x)`

`xcos 20^\circ = 98`

`x = (98)/(cos 20^\circ)`

`x = (98)/(0.9397)`

`x = 104.3`

Answer: GH = 104.3 ft

Answer 2

GH ≈ 104.3 ft

Explanation:

Using the cosine ratio in the right triangle

cos20° =
`(adjacent)/(hypotenuse)` =
`(IG)/(GH)` =
`(98)/(GH)`

Multiply both sides by GH

GH × cos20° = 98 ( divide both sides by cos20° )

GH =
`(98)/(cos20)` ≈ 104.3 ft ( to the nearest tenth )