In each problem, angle C is a right angle. Solve each triangle rounding answers to the nearest tenth.
2) c= 16, b=14​

B = 61°

A = 29°

a = 10

Step-by-step explanation:

We are given;

c = 16, b = 14​

Since we are told that C is a right angle, it means that C = 90°

Thus using sine rule, we have;

c/sin C = b/sin B

16/sin 90 = 14/sin B

16/1 = 14/sin B

sin B = 14/16

sin B = 0.875

B = sin^(-1) 0.875

B ≈ 61°

Now, since C is a right angle, it means that c will be the hypotenuse of the triangle.

Thus, from pythagoras theorem, If the other side of the triangle is a, then;

a² + b² = c²

a² + 14² = 16²

a² = 16² - 14²

a² = 256 - 156

a² = 100

a = √100

a = 10

Since we know B and C, we can find A because sum of angles in a triangle is 180°.

Thus;

A = 180 - (B + C)

A = 180 - (61 + 90)

A = 29°

check the picture below.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.