Question

I need help with this please help

Answer 1

Answer:

a. 3.5 mm

b. 75.5 in.

c. 78.4 ft

Step-by-step 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.

$\sin A = \dfrac{opp}{hyp}$

$\sin 26^\circ = \dfrac{x}{8}$

$x = 8 \sin 26^\circ$

$x = 3.506969...$

$x = 3.5~mm$

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.

$\cos A = \dfrac{adj}{hyp}$

$\cos 58^\circ = \dfrac{40}{x}$

$x\cos 58^\circ = 40$

$x = \dfrac{40}{\cos 58^\circ}$

$x = 75.483...$

$x = 75.5~in.$

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.

$\tan A = \dfrac{opp}{adj}$

$\tan 71^\circ = \dfrac{x}{27}$

$x = 27 \tan 71^\circ$

$x = 78.4136...$

$x = 78.4~ft$

Answer 2

Answer:

a) 3.507

b) 75.48

c) 78.41

Step-by-step 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