In right triangle DEF, ∠E is a right angle, m∠D=26∘, and DF=4.5.
sin26∘≈0.44
cos26∘≈0.90
tan26∘≈0.49
What is the measurement of EF
What is the measurement of EF?
so what's the answer then :/
To find the measurement of EF, we can use the trigonometric function cosine.
In a right triangle, the cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.
Given that the angle D is 26°, and DF is 4.5 units, we can use the cosine function to find the length of EF.
cos(angle D) = adjacent side (EF) / hypotenuse (DF)
Plugging in the values we know:
cos(26°) = EF / 4.5
Using the approximation value for cos(26°) ≈ 0.90:
0.90 = EF / 4.5
To isolate EF, we can multiply both sides of the equation by 4.5:
4.5 * 0.90 = EF
EF ≈ 4.05
Therefore, the measurement of EF is approximately 4.05 units.
To find the measurement of EF in right triangle DEF, we can use the trigonometric functions since we know the values of the angle and the length of one side.
We have the angle D as 26 degrees, and we are given that the side DF has a length of 4.5. To find the length of EF, we can use the trigonometric function sine (sin).
First, we can use sine to find the length of EF. The formula for sine is:
sin(angle) = opposite/hypotenuse
In this case, the angle is 26 degrees, the side opposite is EF, and the hypotenuse is DF. So, we can write:
sin(26 degrees) = EF/4.5
Now, we can rearrange the equation to solve for EF:
EF = sin(26 degrees) * 4.5
Using the approximate value of sin(26 degrees) as 0.44, we can calculate the value of EF:
EF ≈ 0.44 * 4.5
EF ≈ 1.98
Therefore, the measurement of EF is approximately 1.98.
well,
sin 26° = EF/4.5
EF = 4.5sin26°
I assume they want you to do long-hand multiplication, or else why would they give you
the approximation for sin 26°. If you are allowed a calculator, why not use the "best" value
of sin 26° that your calculator can give you?