Question

In ΔGHI, h = 300 inches, ∠G=30° and ∠H=29°. Find the length of i, to the nearest inch.

Answer 1

i ≈ 530 inches (to the nearest inch)

Explanation:

Check the diagram in the attachment. Using sin rule to get the length of i.

According to the rule
`(g)/(sinG) = (h)/(sinH) = (i)/(sinI)\\`

Given h = 300 inches, ∠G=30° and ∠H=29°; we can use the relationship below to get length of i;

`(h)/(sinH) = (i)/(sinI)\\`... 1

Since sum of angle in a triangle is 180°, then ∠G+∠H+∠I = 180°

30°+29°+∠I = 180°

∠I = 180°-(30°+29°)

∠I = 180°-59°

∠I = 121°

Applying equation 1;

`(300)/(sin29^(0) ) = (i)/(sin121^(0) )\\\\300sin121^(0) = iSin29^(0)\\ i = (300sin121^(0))/(Sin29^(0)) \\i = (257.15)/(0.4848) \\i = 530.425inches\\`

i ≈ 530 inches (to the nearest inch)