Question

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

Answer 1

Answer:

i ≈ 530 inches (to the nearest inch)

Step-by-step explanation:

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

According to the rule $\frac{g}{sinG} = \frac{h}{sinH} = \frac{i}{sinI}$

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

$\frac{h}{sinH} = \frac{i}{sinI}$... 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;

$\frac{300}{sin29^{0} } = \frac{i}{sin121^{0} }\\\\300sin121^{0} = iSin29^{0}\\ i = \frac{300sin121^{0}}{Sin29^{0}} \\i = \frac{257.15}{0.4848} \\i = 530.425inches$

i ≈ 530 inches (to the nearest inch)