Question

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

Answer 1

Answer:

5. 34°

6. 29.7

Step-by-step 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

Answer 2

Answer:

5. m∠C ≈ 34°

6. AC ≈ 29.7 metres

Step-by-step 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:

$\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}$

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

$\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}$

$\frac{25}{sin93} =\frac{14}{sinC}$

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