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

User Kzidane
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Answer:

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)

In ΔGHI, h = 300 inches, ∠G=30° and ∠H=29°. Find the length of i, to the nearest inch-example-1
User Rob Avery IV
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