Question

Find x.
Round to the nearest tenth:
31°
у
X
400 ft
x = [ ? ]ft

Answer 1

y = 466.7 ft (nearest tenth)

Explanation:

Using the Alternate Interior Angle Theorem
the angle inside the triangle that is opposite the side
`y` is 31°

Using the cos trig ratio:

`\sf cos(\theta)=(A)/(H)`

where:

• 
  `\theta` is the angle
• A is the side adjacent the angle
• H is the hypotenuse

Given:

• 
  `\theta` = 31°
• A = 400 ft
• H =
  `x`

Substitute given values and solve for x:

`\sf \implies cos(31)=(400)/(x)`

`\sf \implies x=(400)/(cos(31))`

`\sf \implies x=466.7\:ft\:(nearest\:tenth)`

Answer 2

• x = 466.7 ft

• y = 240.3 ft

First find the inner angle:

• 90° - 31°

• 59°

using sine rule:

`\sf sin(x)= (opposite)/(hypotensue)`

`\hookrightarrow \sf sin(59)= (400)/(x)`

`\hookrightarrow \sf x = (400)/(sin(59))`

`\hookrightarrow \sf x = 466.6533`

`\hookrightarrow \sf x = 466.7` ( rounded to nearest tenth )

====================================

using tan rule:

`\sf tan(x)= (opposite)/(adjacent)`

`\hookrightarrow \sf tan(59)= (400)/(y)`

`\hookrightarrow \sf y= (400)/( tan(59))`

`\hookrightarrow \sf y= 240.344`

`\hookrightarrow \sf y= 240.3`