Question

Find the values of x and y to the nearest tenth. Show your work

Answer 1

y = 14.18.

x = 18.51 to the nearest hundredth.

Explanation:

The bottom right side angle is 90 - 50 - 21 = 19 degrees.

cos 19 = y / 15

y = 15 cos 19

= 14.18.

cos (19 + 21) =

cos 40 = y / x

x = y / cos 40

= 14.18 / cos 40

= 18.51.

Answer 2

Answer:x = 18.5

y = 14.2

Explanation:

The given triangle is labelled in the attached photo to make the explanations clearer.

The sum of the angles in a triangle is 180 degrees. Let the unknown angle be # degrees.

This means that

90 + 50 + 21 + # = 180

161 + # = 180

# = 180 - 161 = 19 degrees.

To determine y, we will apply trigonometric ratio

Cos # = adjacent/hypotenuse

Cos 19 = y/15

y = 15cos19 = 15 × 0.9445 = 14.2

To determine x, we will apply trigonometric ratio

Sin 50 = opposite/hypotenuse

Sin 50 = y/x = 14.2/x

xsin50 = 14.2

x = 14.2/sin50 = 14.2/0.7660 = 18.5