105,787 views
1 vote
1 vote
Find x.
Round to the nearest tenth:
31°
у
X
400 ft
x = [ ? ]ft

Find x. Round to the nearest tenth: 31° у X 400 ft x = [ ? ]ft-example-1
User Rozerro
by
2.6k points

2 Answers

13 votes
13 votes

Answer:

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)

User AndersDaniel
by
2.5k points
13 votes
13 votes

Answer:

  • 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

User Ondrej Henek
by
3.4k points