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In ΔXYZ, y = 70 inches, ∠Z=72° and ∠X=17°. Find the area of ΔXYZ, to the nearest 10th of an square inch.

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The area of the triangle XYZ is determined as 681.5 in².

How to calculate the area of the triangle?

The area of the triangle is calculated by applying the following formula as shown below;

∠Y = 180 - (∠X + ∠Z) (sum of angles in a triangle)

∠Y = 180 - ( 17 + 72)

∠Y = 91⁰

The length of side XY is calculated using sine rule as follows;

XY / sin Z = XZ / sin Y

XY / sin 72 = 70 / sin 91

XY = (sin 72 / sin 91 ) x 70 in

XY = 66.6 in

The area of the triangle XYZ is calculated as follows;

A = ¹/₂ (XY) (XZ) sin (X)

A = ¹/₂ x 66.6 in x 70 in x sin (17)

A = 681.52 in²

A = 681.5 in² (1 decimal place)

In ΔXYZ, y = 70 inches, ∠Z=72° and ∠X=17°. Find the area of ΔXYZ, to the nearest 10th-example-1
User Chad La Guardia
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