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olga2289 [7]
3 years ago
13

From the side of a hill wai-kin looks up at the top of a nearby vertical cliff at an angle of elevation of 36 degrees and looks

down at the bottom of the cliff at an angle of depression of 47 degrees. Wai-kin and the cliff are 490 meters apart.
Mathematics
1 answer:
oksano4ka [1.4K]3 years ago
3 0

Answer:

881.5 meters.

Step-by-step explanation:

The horizontal plane at the level of wai-kin's eyes divide the height of the cliff into two parts. Let the upper part be represented by x and the lower part be represented by y.

The height of the cliff = x + y

Applying the appropriate trigonometry functions.

To determine the value of x;

Tan θ = \frac{opposite}{adjacent}

Tan 36^{o} = \frac{x}{490}

⇒ x = 490 x Tan 36^{o}

      = 490 x 0.7265

     = 355.985

x = 356 meters

To determine the value of y;

Tan θ = \frac{opposite}{adjacent}

Tan 47^{o} = \frac{y}{490}

⇒ y = 490 x Tan 47^{o}

      = 490 x 1.0724

      = 525.476

y = 525.5 meters

Therefore,

The height of the cliff = x + y

                                   = 355.985 + 525.476

                                   = 881.461

The height of the cliff is 881.5 meters.

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\bold{\huge{\underline{ Solution\: 2 }}}

  • The name of the circle is <u>IJKL</u>
  • The name of central Angle
  • \sf{\underline{= {\angle} IHJ }}
  • The name of the secant = <u>KL</u>

{\bigstar}Circle :- It is a round figures, which has no end points.

{\bigstar} Central angle :- It the angle ,which lie in the middle of the circle.

  • Here, H is the mid point of the circle .So, Angle IHJ is the central angle.

{\bigstar} Secant :- A line drawn in circle in such a way that it intersect the circle from two distinct points. Then, It is called secant .

  • Here, KL is the line which acts as a secant because it intersect the circle from point K and point L.

\bold{\huge{\underline{ Solution\: 3 }}}

  • Semicircle = FGH and FIH
  • Minor Arc :- FG or GH
  • Major Arc :- FHG or GFH

{\bigstar} Semicircle :- Semicircle is nothing but the half of the circle.

<u>Here</u><u>, </u><u>In </u><u>second </u><u>diagram </u>

  • FGH and FIH are acting as two semicircles which simulatineously forming one circle.

{\bigstar} Minor Arc :- Minor Arc is nothing but the smaller arc of the circle and it is always smaller than the half of the circle that is semicircle.

<u>Here</u><u>, </u>

  • FG or GH are the minor arc of the given circle.

{\bigstar} Major Arc :- Major Arc is nothing but the largest arc of the circle and it is always larger than the half of the circle that is semicircle.

<u>Here</u><u>, </u>

  • FHG or GFH is the major arc as it is larger than the semicircle of the given circle .
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