Question

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

Answer 1

Answer:

• y = 242.4

• x = 437.3

First find the inner angle:

• 90° - 29°

• 61°

[ given hypotenuse = 500 ft ]

using sine rule:

$\sf sin(x)= \dfrac{opposite}{hypotensue}$

$\hookrightarrow \sf sin(61)= \dfrac{x}{500}$

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

$\hookrightarrow \sf x=437.3$

using pythagoras theorem:

• a² + b² = c²

• y² + (437.3)² = 500²

• y = √58760.1

• y = 242.4

Answer 2

Answer:

y = 242.4 ft (nearest tenth)

Step-by-step explanation:

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

Using the sine trig ratio:

$\sf sin(\theta)=\dfrac{O}{H}$

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:

$\sf \implies sin(29)=\dfrac{y}{500}$

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

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