155k views
7 votes
Find y.
Round to the nearest tenth:
290
500 ft
y
X
y = [ ? ]ft

Find y. Round to the nearest tenth: 290 500 ft y X y = [ ? ]ft-example-1

2 Answers

11 votes

Answer:

y = 242.4 ft (nearest tenth)

Explanation:

Using the Alternate Interior Angle Theorem
the angle opposite side
y is 29°

Using the sine trig ratio:


\sf sin(\theta)=(O)/(H)

where:


  • \theta is the angle
  • O is the side opposite the angle
  • H is the hypotenuse

Given:


  • \theta = 29°
  • O =
    y
  • H = 500 ft

Substitute given values and solve for y:


\sf \implies sin(29)=(y)/(500)


\sf \implies y=500sin(29)


\sf \implies y=242.2\:ft\:(nearest\:tenth)

User Sunil Kumar B M
by
8.6k points
9 votes

Answer:

  • y = 242.4
  • x = 437.3

First find the inner angle:

  • 90° - 29°
  • 61°

[ given hypotenuse = 500 ft ]

using sine rule:


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


\hookrightarrow \sf sin(61)= (x)/(500)


\hookrightarrow \sf x=sin(61)*500


\hookrightarrow \sf x=437.3

using pythagoras theorem:

  • a² + b² = c²
  • y² + (437.3)² = 500²
  • y = √58760.1
  • y = 242.4
User Jfbeltran
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories