Question

Find the measurement indicated. Round your answers to the nearest tenth. Use Law of Sines​ or Cosines

Answer 1

5. m∠C ≈ 34°

6. AC ≈ 29.7 metres

Explanation:

5. We need to use the Law of Sines here, which says that for a triangle with sides a, b, and c and angles A, B, and C:

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

Here, a = 25, ∠A = 93°, and c = 14, so we want to find ∠C:

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

`(25)/(sin93) =(14)/(sinC)`

sinC ≈ 0.56

∠C ≈ 34°

6. We need to use the Law of Cosines here, which says that for a triangle with sides a, b, and c and angles A, B, and C:

`c^2=a^2+b^2-2abcosC`

`b^2=a^2+c^2-2accosB`

`a^2=b^2+c^2-2bccosA`

Here, a = 23.2, c = 18.1, ∠B = 91°, and b = x. We want to find b, so:

`b^2=a^2+c^2-2accosB`

`x^2=23.2^2+18.1^2-2*23.2*18.1*cos(91)` ≈ 880.5

x ≈ 29.7 metres

Answer 2

5. 34°

6. 29.7

Explanation:

5. Using sine law

25/sin(93) = 14/sin(C)

sin(C) = 0.5592325395

C = 34.00273934°

6. Using cosine law

AC² = 23.2² + 18.1² - 2(23.2)(18.1)cos(91)

AC² = 880.507229

AC = 29.67334206