Question

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
Triangle D E F with measures as described in the text.

What is the measurement of EF?
If necessary, round your answer to two decimal places, like this: 42.53

Answer 1

Given:

In right triangle DEF, ∠E is a right angle, m∠D = 26°, and DF = 4.5

We need to determine the measurement of EF

Measurement of EF:

The measurement of EF can be determined using the trigonometric ratio.

Thus, the formula is given by

$sin \ \theta=\frac{opp}{hyp}$

Substituting $\theta=26^{\circ}$, $Opp=EF$ and $hyp=DF$

Thus, we have;

$sin \ 26^{\circ}=\frac{EF}{DF}$

Since, it is given that sin 26° ≈ 0.44

Substituting the value of sin in the above equation, we get;

$0.44=\frac{EF}{4.5}$

Multiplying both sides of the equation by 4.5, we get;

$1.98=EF$

Thus, the measurement of EF is 1.98