Lauren was standing on the pier at the beach approach trying
to find her sister. She spotted her at the water’s edge
at an angle
of depression of 28°. If the pier is 5 yards above the sand, how far down
the beach is Lauren’s sister?
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Assuming that the angle at A is the right angle, Pythagoras' theorem says that the length of the hypotenuse (the side opposite the right angle) is the square root of the sum of the squares of the other two sides. In your case, AB and AC are 'the other two sides' and BC is the hypotenuse, so:
/ 2 2 /
length BC = V 10 + 20 = V 100 + 400
= V 500 = 22.36 cm
(To find the angle at C, you need trigonometry and is arc-tan(10/20)
and the angle at B is arc-tan(20/10) - 26.5 deg and 63.5 deg)
The tangent of an angle (in a right triangle) is defined to be the length of the side opposite the angle, divided by the length of the side adjacent to the angle (that is not the hypoteneuse). As the angle approaches 90 degrees, the length of the opposite side gets very large and the length of the adjacent side nears 0. At 90 degrees, the length of the adjacent side is 0, and division by 0 is not defined, so the tangent of 90 degrees is not defined.
Draw a right triangle with the vertical portion of the triangle representing the 37 meters of the light house The base of the triangle is the distance we are trying to find. If the angle of depression is 15 degrees, the other angle is 75 degrees. This is the angle from the boat to the top of the lighthouse.
so The Tangent of 75 degrees is equal to the side opposite the angle (the height of the lighthouse) divided by the side adjacent (the distance we are trying to find.
solving for the distance we get distance = 37 divided by the tangent of 37 degrees
Looking up the tangent of 15 degrees on google give .2679
dividing 137 by .2679=138,1 meters
Hope this helps Loringh PS Please leave a rating for me.