Question

Will give thanks and 5 stars But please show work

Answer 1

Angle = 71.08°

Explanation:

Since we're given all of the sides, we're able to use any one of the trigonometric proportions. I can go through all three to show how they all yield the same answer.

The sine proportion is
`(opposite)/(hypotenuse)`

Using the ? angle as our reference angle (which we can refer to as "a" for the sake of the math), the side measuring 70 units is the opposite side and the side measuring 74 units is the hypotenuse:

`sin (a)=(70)/(74)\\ sin^(-1)=(70)/(74)=a = 71.07535558=71.08`

The cosine proportion is
`(adjacent)/(hypotenuse)`

Using a as our reference angle still, the side measuring 24 units is the adjacent side and the side measuring 74 units is the hypotenuse:

`cos (a)=(24)/(74)\\ cos^-^1=(24)/(74)=71.07535558=71.08`

The tangent proportion is
`(opposite)/(adjacent)`

Using a as our reference angle still, the side measuring 70 units is the opposite side and the side measuring 24 units is the adjacent side:

`tan(a)=(70)/(24)\\ tan^-^1=(70)/(24)=a=71.07535558=71.08`

Again, just use the steps for either one of the three trigonometric proportions