The angle of depression from D to F measures 40°. If EF = 14 yd, find DE. Round your answer to the nearest tenth. 16.7 yd 20.5 yd 11.7 yd 10.7 yd

The problem above is modelled in diagram below

We use the trigonometry ratio to solve length DE

[tex]tan(x)= \frac{DE}{FE} [/tex]
[tex]tan(40)= \frac{DE}{14} [/tex]
[tex]14tan(40)=DE[/tex]
DE=3.36

Answer Link

ApusApus ApusApus · Answer 2 · 2019-05-10T13:36:43+02:00

Answer:

C. 11.7 yards.

Step-by-step explanation:

Please find the attachment.

We have been given that the angle of depression from D to F measures 40°.The length of EF is 14 yd. We are asked to find the length of side DE.

We can see from our attachment that the point D, E and F forms a right triangle, right angles at E. Since line DM is parallel to line Ef, so angle of elevation will be equal to angle of depression.

Since tangent relates opposite and adjacent sides of right triangle, so we can set an equation to find length of DE as:

[tex]\text{tan}(40^{\circ})=\frac{DE}{EF}[/tex]

[tex]0.839099631177=\frac{DE}{14}[/tex]

[tex]0.839099631177*14=\frac{DE}{14}*14[/tex]

[tex]11.747394836478=DE[/tex]

[tex]DE\approx 11.7[/tex]

Therefore, the length of DE is approximately 11.7 yards and option C is the correct choice.