In ΔFGH, the measure of ∠H=90°, the measure of ∠G=75°, and FG = 24 feet. Find the length of HF to the nearest tenth of a foot.

HF ≈ 23.2 ft

Step-by-step explanation:

Using the sine ratio in the right triangle.

sin75° = = =

Multiply both sides by 24

24 × sin75° = HF , thus

HF ≈ 23.2 ft ( to the nearest tenth )

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.