Question

In right triangle DEF, ZE is a right angle, mZD = 26°, and DF = 4.5.

Answer 1

The measurement of EF is 1.98

Explanation:

Given that DEF is a right angled triangle.

Also, given that ∠E is a right angle, m∠D = 26° and DF = 4.5

We need to determine the measurement of EF.

The measurement of EF:

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

Thus, we have,

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

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

Substituting the values, we have,

$sin \ 26=\frac{EF}{4.5}$

Multiplying both sides by 4.5, we get,

$sin \ 26 \times 4.5=EF$

Also, given that sin 26° = 0.44

Thus, substituting the value, we get,

$0.44\times 4.5=DF$

         $1.98=EF$

Thus, the measurement of EF is 1.98