Question

1.) find side BC, ROUND YOUR ANSWER TO THE NEAREST HUNDREDTH

Answer 1

Answer:

Step-by-step explanation:

Triangle ABC is a right angle triangle.

From the given right angle triangle,

AB represents the hypotenuse of the right angle triangle.

With m∠A as the reference angle,

AC represents the adjacent side of the right angle triangle.

BC represents the opposite side of the right angle triangle.

To determine BC, we would apply

the Sine trigonometric ratio.

Sin θ = opposite side/hypotenuse. Therefore,

Sin 40 = BC/3

BC = 3Sin40 = 3 × 0.6428

BC = 1.9

To determine AC, we would apply

the cosine trigonometric ratio.

Cos θ = adjacent side/hypotenuse. Therefore,

Cos 40 = AC/3

AC = 3 × 0.7660

AC = 2.3

Answer 2

Answer:

BC = 2.24 cm

AC = 1.99 cm

Step-by-step explanation:

well to start we have to know the relationships between angles, legs and the hypotenuse.

a: adjacent

o: opposite

h: hypotenuse

sin θ = o/h

cos θ= a/h

tan θ = o/a

θ = 40°

h = 3cm

a = AC

o = BC

first let's calculate BC

sin θ = o/h

o = sin θ * h

o = sin 40 * 3

o = 0.7451 * 3

o = 2.24 cm

BC = 2.24 cm

having one leg and the hypotenuse we can calculate the other leg with pitagoras

h^2 = c1^2 + c2^2

3^2 = 2.24^2 + AC^2

9 = 5.02 + AC^2

AC^2 = 9 - 5.02

AC = √ 3.98

AC = 1.99