Question

Mr. Dominguez is standing on a 40-foot ocean bluff near his home. He can see his two friends on the beach below. If his line of sight is 6 feet above the ground and the angles of depression to his friends are 34° and 48°, how far apart are his friends to the nearest foot?

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

Mr. Dominguez's friends are about 2 feet apart.

Step-by-step explanation:

• This is a problem for right triangles and trigonometric functions. The depression angles for Mr. Dominguez's friends are the angles between the horizontal and his friends' line of sight.
• If we draw a diagram of the situation, we can see that we have two right triangles. The hypotenuse of each triangle is the distance from M.Dominguez each of his friends.
• We can use the tangent function to find the length of each side of any triangle. If we know the angle and length of one leg, we can use the tangent to find the length of the other leg.

We call "d1" the distance between Mr. Dominguez and his first friend and the distance between Mr.Dominguez and his other friend "d2". With the tangent we can set up two equations:

Bronze (34th) = (d1 - 6) / 40th

Bronze (48th) = (d2 - 6) / 40th

We can rearrange each equation to solve for d1 and d2:

d1 = 40*Bronze(34°) + 6

d2 = 40*brown(48°) + 6

Finally, we can subtract these two distances to find the distance between Mr. Dominguez's two friends:

distance = d2 - d1

If we use a calculator to find the tangent of any angle, we get:

d1 = 35.26 feet

d2 = 33.28 feet

distance ≈ 1.98 feet

Therefore, Mr. Dominguez's friends are about 2 feet apart.

Learn more about trigonometric functions :

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