Question

Find each measurement indicated. Round your answers to the nearest tenth. Please show your work. Part 2

4. Find AC

5. Find BC

6. Find AC​

Answer 1

4. 14.0

5. 19.3 km

6. 20.0 m

Explanation:

4. using sine law

AC/sin21 = 30/sin130

AC = (30/sin130) × sin21

AC = 14.03448401

5. BC/sin123 = 9/sin23

BC = (9/sin23) × sin123

BC = 19.31772147

6. AC/sin65 = 22/sin88

AC = (22/sin88) × sin65

AC = 19.95092488

Answer 2

4. 14.03 miles

5. 15.02 kilometers

6. 19.95 meters

Explanation:

4. We need to use the law of sines, which states that for a triangle with angles A, B, and C and sides a, b, and c, respectively, then:

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

Here, a = 30, <A = 130, and <B = 21. So, let's plug these in:

`(30)/(sin130) =(b)/(sin21)`

b = AC =
`(30)/(sin130)*{sin21}` ≈ 14.03 miles

5. Here, c = 7, <C = 23, and <A = 123. We want to find BC, which is just a:

`(7)/(sin23) =(a)/(sin123)`

a = BC =
`(7)/(sin23) *{sin123}` ≈ 15.02 kilometers

6. Here, c = 22, <C = 88, and <B = 65. We want to find AC, which is just b:

`(22)/(sin88) =(b)/(sin65)`

b = AC =
`(22)/(sin88) *{sin65}` ≈ 19.95 meters

Hope this helps!