Question

I need help with this please help

Answer 1

a. 3.5 mm

b. 75.5 in.

c. 78.4 ft

Explanation:

a.

x is opposite the 26-deg acute angle.

8 mm is the hypotenuse.

The trigonometric ratio that relates the opposite leg to the hypotenuse is the sine ratio.

`\sin A = (opp)/(hyp)`

`\sin 26^\circ = (x)/(8)`

`x = 8 \sin 26^\circ`

`x = 3.506969...`

`x = 3.5~mm`

b.

The 40-inch leg is adjacent to the 58-deg acute angle.

x is the hypotenuse.

The trigonometric ratio that relates the adjacent leg to the hypotenuse is the cosine ratio.

`\cos A = (adj)/(hyp)`

`\cos 58^\circ = (40)/(x)`

`x\cos 58^\circ = 40`

`x = (40)/(\cos 58^\circ)`

`x = 75.483...`

`x = 75.5~in.`

c.

For the 71-deg acute angle, 27 ft is the adjacent leg, and x is the opposite leg. The trigonometric ratio that relates the opposite leg to the adjacent leg is the tangent ratio.

`\tan A = (opp)/(adj)`

`\tan 71^\circ = (x)/(27)`

`x = 27 \tan 71^\circ`

`x = 78.4136...`

`x = 78.4~ft`

Answer 2

a) 3.507

b) 75.48

c) 78.41

Explanation:

Problem A

The opposite side of the angle and the hypotenuse are involved in the question. Therefore you will be using the sine.

sin(26) = x / 8 Multiply both sides by 8

8*sin(26) = x Sin(26) = 0.4384

8*0.4384 = x Do the multiplication

3.507 = x

Problem B

The side adjacent and the hypotenuse are used in this problem. The angle is given, so you are working with the cosine.

Cos(58) = adjacent / hypotenuse

Cos(58) = 0.5299

0.5299 = 40/x Multiply both sides by x

0.5299 x = 40 Divide both sides by 0.5299

x = 40 / 0.5299

x = 75.48

Problem C

The opposite side and the adjacent side are involved and the angle is given.

Tan(71) = opposite / adjacent

tan(71) = 2.904

2.904 = x / 27 Multiply both sides by 27

2.904 * 27 = x Combine

x = 78.414