Question

Find the measure of the indicated angle to the nearest degree.

Answer 1

? ≈ 62°

Explanation:

using the sine ratio in the right triangle

sin? =
`(opposite)/(hypotenuse)` =
`(39)/(44)` , then

? =
`sin^(-1)` (
`(39)/(44)` ) ≈ 62° ( to the nearest degree )

Answer 2

62°

Explanation:

We use the fact that the ratio of the sides of the triangle to the angles opposite them is given by the Law of Sines:

"In any triangle, the ratio of a side length to the sine of its opposite angle

is the same for all three sides"

`(a)/(sinA) = (b)/(sinb) =(c)/(sinC)`

where A is the is the angle opposite side a, B the angle opposite to side b, C is the angle opposite to side c

For the given triangle we get
44/sin90 = 39/sin?

sin90 is 1 so we get 44/1 = 39/sin?

or cross-multiplying,

sin? = 39/44 = 0.886363..

? = sin⁻¹ (0.886363) = 62.42° ≈ 62° answer