Question

Find the angle in degrees, rounded to one decimal.
°

Answer 1

Check the picture below.

`\sin(\theta )=\cfrac{\stackrel{opposite}{40}}{\underset{hypotenuse}{90}}\implies \sin(\theta )=\cfrac{4}{9}\implies \theta =\sin^(-1)\left( \cfrac{4}{9} \right)\implies \theta \approx 26.4^o`

Make sure your calculator is in Degree mode.

Answer 2

Θ ≈ 26.4°

Explanation:

using the sine ratio in the right triangle

sinΘ =
`(opposite)/(hypotenuse)` =
`(40)/(90)` =
`(4)/(9)` , then

Θ =
`sin^(-1)` (
`(4)/(9)` ) ≈ 26.4° ( to 1 decimal place )