{"id":4650,"date":"2021-11-28T12:59:44","date_gmt":"2021-11-28T12:59:44","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=4650"},"modified":"2022-01-03T08:19:50","modified_gmt":"2022-01-03T08:19:50","slug":"angle-of-depression-with-examples-and-faqs","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/angle-of-depression-with-examples-and-faqs\/","title":{"rendered":"Angle of Depression with Examples and FAQs"},"content":{"rendered":"

[et_pb_section fb_built=”1″ admin_label=”Section” module_class=”mainsec” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#e0f2fd” z_index=”1″ custom_padding=”5px||5px||true|false” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_row column_structure=”3_5,2_5″ custom_padding_last_edited=”on|phone” _builder_version=”4.10.8″ _module_preset=”default” background_color=”#FFFFFF” width=”100%” max_width=”1310px” custom_padding=”|51px|40px|51px|false|true” custom_padding_tablet=”” custom_padding_phone=”|40px|30px|40px|false|true” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}”][et_pb_column type=”3_5″ admin_label=”Column L” _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_text admin_label=”Acute Angles
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Angle of Depression with Examples and FAQs<\/h1>\n

[\/et_pb_text][et_pb_text admin_label=”Text” _builder_version=”4.13.1″ _module_preset=”default” text_font_size=”16px” header_2_font=”|600|||||||” header_2_text_color=”#a01414″ header_3_font=”|600|||||||” custom_padding=”15px|15px|54px|4px|false|false” global_colors_info=”{}”]<\/p>\n

What is an Angle of Depression?<\/b><\/h2>\n

The Angle of Depression is the angle between the line of sight of the object and the observer and the horizontal line of the level at which the observer is above the object.<\/span><\/p>\n

\"\"<\/span><\/p>\n

From the diagram above we can see that an Observer is higher than the Object, and the line of sight is also depicted.\u00a0<\/span><\/p>\n

Now, the angle <\/span>\u03b8<\/span> formed by the line of sight and the line horizontal to the observer is the angle of depression.<\/span><\/p>\n

From the diagram, we can see that if a perpendicular is dropped from the object point on the horizontal line a right-angled triangle is formed. Hence, using the trigonometric ratios and properties of the right-angled triangle we can easily find the angle of depression if the distance between the object and observer and the height is given.<\/span><\/p>\n

<\/h2>\n

The formula for Angle of Depression<\/b>\u00a0<\/b><\/h2>\n

The angle of depression can be easily calculated if the length of any two sides of the above triangle is known to us, by using the inverse of trigonometric functions.<\/span><\/p>\n

\"\"<\/span><\/p>\n

From the above diagram the length of the sides of the triangle are mentioned, from this, we can easily get the angle of depression(<\/span>\u03b8<\/span>) with the help of the following inverse trigonometric ratios.<\/span><\/p>\n

We know,\u00a0<\/span><\/p>\n

\\sin \\theta=\\frac{\\text { perpendicular }}{\\text { hypotenuse }} <\/span><\/span><\/p>\n


\\cos \\theta=\\frac{\\text { base }}{\\text { hypotenuse }} <\/span><\/span><\/p>\n


\\tan \\theta=\\frac{\\text { perpendicular }}{\\text { base }}<\/span><\/span><\/p>\n

 <\/p>\n

From the figure above:<\/span><\/p>\n


\\sin \\theta=\\frac{b}{a}<\/span><\/span><\/p>\n


\\cos \\theta=\\frac{c}{a} <\/span><\/span><\/p>\n

<\/span><\/p>\n\\tan \\theta=\\frac{b}{c} <\/span>\n

 <\/p>\n

Hence, the value of <\/span>\u03b8<\/span> is:<\/span><\/p>\n

\\theta=\\sin ^{-1}\\left(\\frac{b}{a}\\right) <\/span><\/span><\/p>\n


\\theta=\\cos ^{-1}\\left(\\frac{c}{a}\\right)<\/span><\/span><\/p>\n

 <\/p>\n

\\theta=\\tan ^{-1}\\left(\\frac{b}{c}\\right)<\/span><\/span><\/p>\n

Thus, when the length of any two sides is known the value of <\/span>\u03b8<\/span> can easily be calculated.\u00a0<\/span><\/p>\n

<\/span><\/p>\n

How do you differentiate between the angle of elevation and depression?<\/b><\/h2>\n

If a person(observer) is standing at a distance and at a height above the surface of the object he is looking at, then an angle is formed by the line of sight and the line horizontal to the observer which is the angle of depression. Whereas, if a person(observer) is standing lower than the object and at a distance from the object angle of elevation is formed.<\/span><\/b><\/p>\n

\"\"<\/span><\/b><\/p>\n

In the figure above the Observer is looking at two objects, that are:<\/span><\/p>\n