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SVEN [57.7K]
3 years ago
12

What is the value of x?​

Mathematics
1 answer:
alina1380 [7]3 years ago
7 0

Answer:

<h2>x = 4</h2>

Step-by-step explanation:

Look at the picture.

We have the triangles 30° - 60° - 90° and 45° - 45° - 90°.

The sides are in proportions:

30° - 60° - 90° ⇒ 1 : √3 : 2

45° - 45° - 90° ⇒ 1 : 1 : √2

======================================================

SR=ST\sqrt3\to ST\sqrt3=2\sqrt3\qquad\text{divide both sides by}\ \sqrt3\\\\ST=2\\\\TR=2ST\to TR=2(2)=4\\\\RQ=TR\to RQ=4\to x=4

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<h3>What is angle of elevation?</h3>

What you see something higher than your eye level height, you need to see up, you elevate your head to see that thing. The angle from the straight horizontal level of eye to the current elevated level is measured and named as angle of elevation.

Similarly, there is angle of depression when the observer looks down.

<h3>How to calculate the height of the considered lighthouse?</h3>

See the figure attached below to understand the symbols used in calculations.

Let the boat is on point C, and let the light house be AB.

Then we have:

Length of CA = 120 meters

∠ ACB = 40°

To find: length of AB

By using the trigonometric ratio tangent, we get:

tan(\angle ACB) = \dfrac{AB}{AC}\\\\tan(40^\circ) = \dfrac{h}{120}

Since here h is denoted by y, we have h = y, or

The equation to find the height of the lighthouse is

tan(40^\circ) = \dfrac{y}{120}

Thus,

The length (y) of the lighthouse is given by:

Option D:  tan 40° = y over 120.

Learn more about angle of elevation here:

brainly.com/question/12483071

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