Question

Find the value of w and then x. Round lengths to the nearest tenth and angle measures to the nearest degree.

Answer 1

w=7.6

x=43.7

Explanation:

To solve for w you can use Sin(x)=
`(Opposite)/(Hypotenuse)` which would basically be Sin(50)=
`(w)/(10)` then solve. Multiply the ten on both sides so you have 10*Sin(50)=w and your final answer is 7.6

To solve for x you can also use Sin(x)=
`(7.6)/(11)` then just use Inverse of Sin^-1

The answer is x=43.7

Answer 2

Explanation:

The diagram contains 2 right angle triangles.

To determine w, we would apply the the Sine trigonometric ratio. It is expressed as

Sin θ = opposite side/hypotenuse.

Hypotenuse = 10

Opposite side = w

Therefore

Sin 50 = w/10

w = 10Sin50 = 10 × 0.7660

w = 7.66

To determine angle x, we would also apply the sine trigonometric ratio. Therefore

Hypotenuse = 11

Opposite side = 7.66

Sin x = 7.66/11 = 0.6964

x = Sin^-1 (0.6964)

x = 41.1 degrees to the nearest tenth.