Question

Using laws of Sines. Find the measurement indicated. Round your answers to the nearest tenth.​

Answer 1

AB = 28 ft; m<A = 24 deg

Explanation:

8.

Since you are not given an angle and its opposite side, you cannot start with the law of sines. You must use the law of cosines.

`c^2 = a^2 + b^2 - 2ab \cos C`

`c^2 = (14~ft)^2 + (24~ft)^2 - 2(14~ft)(24~ft) \cos 91^\circ`

`c^2 = 196~ft^2 + 576~ft^2 - 672~ft^2(-0.01745)`

`c = √(783.73~ft^2)`

`c = 27.995~ft`

AB = c = 28 ft

9.

`(\sin A)/(a) = (\sin B)/(b) = (\sin C)/(c)`

`(\sin A)/(a) = (\sin B)/(b)`

`(\sin A)/(9~km) = (\sin 84^\circ)/(22~km)`

`\sin A = (9~km~\sin 84^\circ)/(22~km)`

`\sin A = 0.40685`

`A = \sin^(-1) 0.40685`

`A = 24^\circ`

Answer 2

see below

Explanation:

8.

We have to use the law of cosines to find AB

c^2 = a^2 + b^2 − 2ab cos(C)

AB^2 = 14^2 + 24^2 - 2 * 14 *24 cos(91)

AB^2 =196 +576 - 672 cos(91)

AB^2 =783.7280171

Taking the square root of each side

AB =27.99514

Rounding to the nearest tenth

AB = 28

(If the lengths are supposed to have the variable A)

AB = 28A

9.

Using the law of sines

sin 84 sin A

-------------- = -------------

22 9

Using cross products

9 sin 84 = 22 sin A

Divide each side by 22

9 sin 84 /22 = sin A

.406849866 = sin A

Taking the inverse sin of each side

24.00710132 = A

To the nearest tenth

A = 24