Sharon is taking part on a dolphin watch on the coast, she stands on the top of the cliff of height 30 m. Her?

Question

Sharon is taking part in a dolphin watch on the coast, she stands on the top of a cliff of height 30m. Her height to her eye level is 1.6 m. She observes a dolphin at an angle of depression of 30 degrees.
She wishes to know the distance of the dolphin from the base of the cliff?

Answer 1

The total height of her eyes above the surface of the water is 30 + 1.6 = 31.6 m.

The angle of depression is related to the distance to the dolphin by the tangent. The height of Sharon's eyes above the water is the opposite, and the horizontal distance to the dolphin is the adjacent. (If this isn't obvious from the drawing, remember from geometry that alternate interior angles are congruent.)

tan 30 = 31.6/d
d = 31.6/tan 30 = 54.73 meters

Answer 2

The adjacent side is the 31.6 meters. . This is angle B. Susan is at the top of the cliff. The angle of depression is 30° . The opposite side is the distance from the dolphin to the cliff.

tanθ =a / o

tan30 = 31.5 / o

0tan30 = 31.6

otan30 / tan 30 = 31.6 / tan 30

o = 31.6 / 0.577350269

0 = 54.73280552 meters

The answer is: the distance from the dolphin to the base of the cliff is 54.73 Meters rounded to two decimal places.

- - - - - - - - - - - - - - - - - -

I made a mistake in the caculation

The opposite side is directly across from th 30° vertex

The adjacent side is the ray from the 30° vertex towards the 90° angle.

tanθ = o/a

tan30 = o / 31.6

31.6(0.577350269) = o

18.24426851 m = o

The answer is o = 18.24m Rounded to two decimal places

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Answer 3

The overall height is 30m + 1.6m = 31.6 m
By parallel lines the angle of depression (30 degrees) is the same as the angle of elevation from sea-level.(by alternate angles).
NB the line of sight is the intercept of two parallel lines. One of the parallel lines is the surface of the sea, and the other parallel line is from the viewers eye to the horizon.

Using trigonometry :-

Tan 30 degrees = opposite/ADJACENT = Vertical height/distance from dolphin to base of the cliff.

So!!!!
Tan 30 degrees = 31.6m/distance from dolphin to Cliff base.
by algebraic rearrangement :-
Distance from dolphin to cliff base = 31.6 m / TAN 30 DEGREES

- DO - DO - = 31.6 m./0.577350269

- do - do - = 54.73280552 m.

or 54.73 m (2 d.p.) It would be trivial to put in any more decimals because the size of the cliff and the dolphin would be measured in metres, and not thousandths of a metre.

Answer 4

The best trick I use to resolve these trigonometry word problems is to draw the right angle triangle that depicts what is being said.

Then show the values of the angle(s) that are provided if any.
Lastly, show the values of the side(s) that are provided.

Remember that all you need is one side and one of the 2 angles or
2 of the sides.
With this information, you can find the missing angle(s) and/or sides.
Of course, you need to know that Sine is Hyp/Opp; Cosine is Hyp/Adj; and Tangent is Opp/Adj.
I learnt a 6-word phrase that helps me remember the latter. The first letter of each word represents the first letter of Sine, Cosine, Tangent sides in the same sequence.
This phrase is: "Oscar Has A Heap Of Apples"

God luck with all future similar problems. .

Answer 5

everywhere interior the stands with the help of a procedures beats the field seats (apart from sitting interior the blistering August warmth on an afternoon recreation) THEN i'd evaluate the AC of the field. i love the bleachers and the prospect to come back residing house with a HR ball, or everywhere else interior the park and catching a foul ball. The smell of the nutrition contained in the ballpark is continually large too.

Answer 6

tan (90 - 30) = opposite / adjacent

tan 60 = distance / 31.6

tan 60 * 31.6 = distance

distance = 54.7 m

Answer 7

54.73 meters
Use this formula:
Tangent of 30°= 31.6 (opposite) / adjacent

Answer 8

whos sharon ??
lol