Question

Find DE.I dont understand these questions so this is an example

Answer 1

We can answer this question using trigonometric ratios. This is possible because we have a right triangle in the question (we can check this by looking at the small square between the sides DE and EF).

We also need to have into account the reference angle. The reference angle here is the angle mHaving all this information, we have that the trigonometric ratios are the sine, the cosine, and the tangent, and they are defined, respectively as follows:

`\sin (\theta)=\frac{\text{opp}}{\text{hyp}}`
`\cos (\theta)=(adj)/(hyp)`
`\tan (\theta)=(opp)/(adj)`

As we can see, the sine is the ratio between the opposite side to the reference angle over the length of the hypotenuse, the cosine the ratio between the adjacent side to the reference angle to the hypotenuse, and the tangent is the ratio between the opposite side to the reference angle to the adjacent side to this reference angle.

We are asked for the side DE. This side is opposite to the reference angle 30. We have that the hypotenuse is equal to 16. Therefore, we need to use the sine ratio to solve this triangle. Remember: you can only use this trigonometric ratio in case of having a right triangle.

Then, we have:

`\sin (30)=(DE)/(DF)=(DE)/(16)\Rightarrow DE=\sin (30)\cdot16`

And we know that sin(30) = 1/2. Then, we have:

`DE=(1)/(2)\cdot16\Rightarrow DE=(16)/(2)\Rightarrow DE=8`

Therefore, the side DE (one of the legs of the right triangle) is equal to 8, DE = 8.