Question

Please find the value of x and round to the nearest tenth

Answer 1

x = 2,879.4 m

Explanation:

Find the measure of the angle formed by the horizontal line and line x:

What we know:

• This angle is an olive green in the image attached
• This angle is an angle of depression
• The angle of elevation measures 10°
• Angles of depression and elevation are congruent because they are alternate interior angles

Therefore, this angle measures 10 degrees.

Find the value of x:

Now that we have our angle, we can find x. The side opposite the 10 degree angle is 500 m long. The hypotenuse is x. We can use the sine ratio to find x.

Substitute:

sinx = opp/hyp

sin10 = 500/x

Multiply x on both sides:

x(sin10) = (500/x)x

x(sin10) = 500

Divide by sin10 on both sides:

x(sin10) = 500

/sin10 /sin10

x = 2,879.4 m

or

Find the measure of the angle formed by the side x and the side that measures 500 m:

What we know:

• In the image attached, the angle is teal
• The angle that complements it measures 10°
• The measure of both angles = 90°

To find the measure of the angle, subtract.

90 - 10 = 80

The angle is 80°

Find the value of x:

Now that we have our angle, we can find x. The side adjacent to the 80 degree angle is 500 m long. The hypotenuse is x. We can use the cosine ratio to find x.

Substitute:

cosx = adj/hyp

cos80 = 500/x

Multiply x on both sides:

x(cos80) = (500/x)x

x(cos80) = 500

Divide by cos80 on both sides:

x(cos80) = 500

/cos80 /cos80

x = 2,879.4 m

Answer 2

x ≈ 2879.4 m

Explanation:

The bottom right side angle of the triangle is alternate to the 10° angle

Using the sine ratio in the right triangle

sin10° =
`(opposite)/(hypotenuse)` =
`(500)/(x)`

Multiply both sides by x

x × sin10° = 500 ( divide both sides by sin10° )

x =
`(500)/(sin10)` ≈ 2879.4 ( to the nearest tenth )