Question

Work out the length x in the triangle

Answer 1

x = 16

Explanation:

the area (A) of the triangle is calculated as

A =
`(1)/(2)` absinC

where a, b are 2 sides of the triangle and C the angle between them

here a = 15, b = x, C = 30° and A = 60 , then

`(1)/(2)` × 15 × x × sin30° = 60

7.5x ×
`(1)/(2)` = 60 ( multiply both sides by 2 to clear the fraction )

7.5x = 120 ( divide both sides by 7.5 )

x = 16

Answer 2

• The length x is 16 m

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Imagine the height of the triangle is h, which is perpendicular to 15 m side.

The area is:

• A = bh/2

Use this formula and given values and find the value of h:

• 60 = 15h/2
• h = 60*2/15
• h = 8 m

Since h is opposite to 30° angle and x is the hypotenuse of the formed right triangle, we'll use the property of 30°x60°x90° triangle.

• Hypotenuse is twice the length of the side opposite to 30° angle.

In our case h is opposite to 30° angle, therefore we have:

• x = 2h = 2*8 = 16 m