Question

Find angle A !!

*law sines and cosines*
2.

Answer 1

HI,

Explanation:

Using law of sinus:

`\frac{sin (\widehat{A})}{BC} =\frac{sin (\widehat{B})}{AC} \\\\sin(\widehat{A})=(25*sin(62^o))/(28) =0.78893406...\\\\m\angle{A}=arcsin(0.7889...)=52.031216..^o`

Answer 2

∠ A ≈ 52°

Explanation:

using the law of sines in Δ ABC

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

where a, b and c are the sides opposite ∠ A, ∠ B and ∠ C

here a = 25 and b = 28

using the first 2 ratios from the law of sines to find ∠ A

`(25)/(sinA)` =
`(28)/(sin62)` ( cross- multiply )

28 × sinA = 25 × sin62° ( divide both sides by 28 )

sinA =
`(25sin62)/(28)` , then

∠ A =
`sin^(-1)` (
`(25sin62)/(28)` ) ≈ 52° ( to the nearest degree )