Question

Pls help asap it’s annoying me

Answer 1

b. 53.1°

c. 126.9⁰

Explanation:

These are SSA triangles; use Law of Sines to find the unknown angle:

b) sin30/15 = sinA/24

sinA(15) = sin30(24)

sinA = sin30(24)/15 = 0.80

m∠A = sin⁻1(0.80) = 53.1°

c) m∠A = 180 - 53.1 = 126.9⁰

Answer 2

∠ BAC = 53.13° , ∠ BAC = 126.87°

Explanation:

using the Sine rule in Δ ABC

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

where a is the side opposite ∠ A and c is the side opposite ∠ C

here a = BC = 24 and c = AB = 15 , then

`(24)/(sinA)` =
`(15)/(sin30)` ( cross- multiply )

15 sinA = 24 sin30° ( divide both sides by 15 )

sin A =
`(24sin30)/(15)` , then

A =
`sin^(-1)` (
`(24sin30)/(15)` ) = 53.13°

(b)

acute angle BAC = 53.13°

(c)

the sine of an angle is positive in both the first and second quadrant , so

obtuse angle BAC = 180° - 53.13° = 126.87°