Question

A falcon flying at a height of 200 yards spots a sparrow flying at a height of 150 yards. The location of the sparrow makes an angle of 40° from the horizontal line through the falcon's location. What is the distance x between the falcon and the sparrow? Assume that the ground beneath the birds is level.

Answer 1

Do you have any answer choices?

Answer 2

exactly

Answer 3

A).43 yards
B).60 yards
C).65 yards
D).78 yards

Answer 4

Okay um this might help
Sin(40)=opposite- leg/hypotenuse
opposite=200
leg=50
idk if this is right but I hope it helps in someway

Answer 5

I mean leg=150*

Answer 6

So, does this diagram help?

Answer 7

yea

Answer 8

Alrighty, can you Eliminate any of them?

Answer 9

Can you eliminate any of the choices based on the information that was given to you?

Answer 10

Well, tell me why, It doesn't have to be a long explanation. Just give me verification that you are understanding why you eliminated that.

Answer 11

so what we want is

Answer 12

So at the end we have our reference angle, opposite side, and hypotenuse

We know that \[\sin(\theta) = \frac{opposite}{hypotenuse}\] \[\cos(\theta) = \frac{adjacent}{hypotenuse}\] \[\tan{\theta} =\frac{opposite}{adjacent}\]

Answer 13

And so with these, trig ratios, and knowing we want opposite and hypotenuse, which trig ratio should we use @troublekiddseyy

Answer 14

After you choose the correct one, you plug in the reference angle, the opposite side, and x into the equation, and then at the end finding the value of x
then round to the nearest wholenumber