Question

Question 1: Please help, look at the picture below.

Answer 1

Answer:

1.98

Step-by-step explanation:

The triangle in the figure is a right triangle, which has a 90 degrees angle.

The side opposite to the right angle is called hypothenuse, and it is the longest side of the triangle.

For a right triangle, the following relationship exists between angles and sides:

$sin \theta = \frac{opposite}{hypothenuse}$ (1)

$cos \theta=\frac{adjacent}{hypotenuse}$

where $\theta$ is any of the other 2 angles in the triangle, and opposite means "side opposite to the angle" and adjacent means "side adjacent to the angle".

In this problem, we know that the angle at D is

$\theta=26^{\circ}$

We also know that the hypothenuse is

$hypothenuse=DF=4.5$

Therefore, in order to measure EF, we can use eq.(1). We find:

$sin \theta = \frac{EF}{DF}\\EF=DF sin \theta = (4.5)(sin 26^{\circ})=1.98$